Counting Hours, Counting Losses: The Toll of Unpredictable Work Schedules on Financial Security
Authors: Pegah Nokhiz
Aravinda Kanchana Ruwanpathirana
Aditya Bhaskara
Suresh Venkatasubramanian
Venue: Accepted by TMLR ()

Abstract: Financial instability is a pressing concern in the United States, with drivers that include growing employment disparities and insufficient wages. While research typically focuses on financial aspects such as income inequality in precarious work environments, there is a tendency to overlook the time-related aspect of unstable work schedules. The inability to rely on a consistent work schedule not only leads to burnout and conflicts between work and family life but also results in financial shocks that directly impact workers' income and assets. Unforeseen fluctuations in earnings pose challenges in financial planning, affecting decisions regarding savings and spending, and ultimately undermining individuals' long-term financial stability and well-being. 

Our objective in this study is to understand how unforeseen fluctuations in earnings exacerbate financial fragility by investigating the extent to which individuals' financial management depends on their ability to anticipate and plan for future events. To answer this question, we present a computational framework to model real-time consumption decisions under income uncertainty, drawing on advances in online planning and reinforcement learning (RL) with lookahead. We introduce a novel online algorithm that enables utility-maximizing agents to dynamically adapt consumption choices in response to financial shocks, leveraging partial deterministic information about future income. This approach forms the basis of our simulation framework, which models how workers manage consumption in the face of variable work schedules and the imperative to avoid financial ruin.

Through theoretical analysis, we quantify the utility advantage conferred by varying levels of lookahead. Empirical simulations demonstrate how increased lookahead improves financial utility. That is, with this framework, we demonstrate both theoretically and empirically how a worker's capacity to anticipate schedule changes enhances their long-term utility. Conversely, the inability to predict future events can worsen workers' financial instability. Moreover, our framework enables us to explore policy interventions aimed at mitigating the problem of schedule uncertainty. By modeling both individual behavior and potential policy interventions (e.g., advance scheduling regulations), our framework draws on ideas from machine learning and reinforcement learning to inform economic questions surrounding information access in financial planning.

Published in Transactions on Machine Learning Research (07/2025)
Counting Hours, Counting Losses: The Toll of Unpredictable Work Schedules on Financial Security
Pegah Nokhiz"
pegoh.nokhie@gmalllcom
Cornell University, Cornell Tech.
Aravinda Kanchana Ruwanpathirana"
kanchann.. wwwrchowww.waaappptteeammoaammaa
National Universily of Singapore
Aditya Bhaskara University of Utah
Mhaskaraaddtyo@@gaikk.com
Suresh Venkatasubramanian Brown University
swresh_ www.sseeeenkkttssbbmmmaaaaoaoooe
Reviewed OpenReview: https: htttes///pperreviau
openreview. net/ pet/formm? id= PEZx219hiP
Abstract
Financial instability is pressing concern in the United States, with drivers that include growing employment disparities and insufficient. wages. While research lypically focuses on financial aspects such as income inequality in precarious work environments, there a tendency to overlook the time-related aspect of unstable work schedules. The inability to rely on consistent work schedule not only leads to burnout and conflicts between work and family life but also results in financial shocks that directly impact workers' income and assets. Unforeseen fluctuations in earnings pose challenges in financial planning, affecting decisions regarding savings and spending, and ultimately undermining individuals' long-term financial stability and well-being.
Our objective in this study is understand how unforeseen fluctuations in earnings exacer- bate financial fragility by investigating the extent to which individuals' financial management depends on their ability to anticipate and plan for future events. To answer I this question, we present a computational framework to model real-time consumption decisions under income uncertainty, drawing on advances in online planning and reinforcement learning (RL) with lookahead. We introduce a novel online algorithm that enables maximizni agents to dynamically adapt consumption choices in response to financial shocks, leveraging partial deterministic information about future income. This approach forms the basis of our sim- ulation framework, which models how workers manage consumption in the face of variable work schedules and the imperative to avoid financial ruin.
Through theoretical analysis, quantify the utility advantage conferred by varying levels of lookahead. Empirical simulations demonstrate how increased lookahcad improves financial utility. That is, with this framework, we demonstrate both theoretically and empirically how a worker's capacity to anticipate schedule changes enhances their long-term utility. Conversely, the inability to predict future events can worsen workers' financial instability. Moreover, our framework enables us to explore policy interventions aimed at mitigating the problem of schedule uncertainty. By modeling both individual behavior and potential policy interventions (c.g., advance scheduling regulations), framework draws idcas
"The first authors contributed equally this work.

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from machine learning and reinforcement learning to inform economic questions surrounding information access in financial planning.
1 Introduction
Financial instability is persistent challenge for many workers in the U.S., driven not only by stagnant wages and limited benefits, but also by irregular and unpredictable work schedules (Weller) 2018 Kalleberg 2009; 2011 In sectors like food service and retail, such volatility is the norm: over 80% of workers report having little to no control over their schedules, and a majority are required to remain perpetually available for shifts [ooginn 2020 Schneider & Harknett 2019b). This unpredictability severely limits workers' ability to plan ahead financially, with more than half of income volatility cases traced to erratic scheduling (McCrate 2018
These dynamics pose a real-time computational challenge under uncertainty: individuals must make daily consumption and savings decisions in real time, while facing uncertainty about future income. Workers earn income through their employment and use it to fulfill daily necessities. How individuals allocate their income across various needs determines the utility they derive, based on how effectively they balance saving and consumption. Since income is impacted by umpredictable work schedules, the challenge becomes one of optimizing consumplion policies without full information about fulure earnings. This motivates a technical inquiry into quantifying the utility loss from income volatility and systematically evaluating the impact of limited foresight on financial outcomes.
Therefore, this leads to a need for a computational model that captures how individuals optimize consumption and savings in response to unpredictable schedules. The model must jointly represent the utility-maximizing behavior of agents under uncertainty and varying levels of lookahead.
Subsequently, we develop a computational model of decision beckiign-making that frames consumption under uncer- tainty as an online planning problem. Agents aim to maximize utility while facing stochastic income and financial shocks. Unlike classical economic models that assume full knowledge of future income (Deaton et al. 1992; Deaton 1989), our approach models agents with partial lookahead: they receive determinis- tie information about income within a fixed horizon and stochastic information beyond the horizon. This formulation would allow examining how varying the amount of available future information affects utility outcomes and adaptive decision-making under uncertainly.
This modeling approach is advantageous for several reasons. First, offiine models generate a singular, fixed policy incapable of adapting to new financial information/shocks. Secondly, the simultancous occurrence of financial data availability and optimization better aligns with real-world behavior. Third, the roducttion of future lookahead allows for a nuanced exploration of its utility under different conditions and param- eters (i.e., various levels of lookahead). Lastly, the online framework with future information provides a robust simulation environment for studying the consequences of work schedule instability and bias in future information availability. Our model is particularly relevant in light of recent regulatory efforts aimed at improving clarity in work scheduling (e.g., the Retail Workers Bill of Rights (Golden] 2015)), which aim to provide workers with more predictable incomes. By empirically exploring policy-driven interventions (e.g.. increasing lookahead), we offer insights into how technical tools can evaluate and potentially inform policy decisions.
Technical Framing and ML/RL Positioning. Our setup connects naturally to work reinforcement learning (RL) and machine learning (ML), where lookahead is a well-established technique for improving sequential decision-making under uncertainty by estimating the long-term consequences of actions, rather than relying solely on immediate outcomes. More formally, RL often studies H--ste lookahead, where the agent optimizes its actions by considcring the expected utility over H steps (Sikchi et al., 2022). This paradigm has been extensively studied, with numerous works examining the role of lookahead with fixed horizons (Moerland et al. 2020 Sikchi et al. 2022; Dalal et al. 2021 Efroni et al.) 2018). We explore a related but distinct form of lookahead. Rather than evaluating expected utility over fixed horizon, we consider agents who are given exact knowledge of events within a fixed horizon and stochastic information beyond it, which they use to guide decision-making.
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also explores similar concept of lookahead in RL with partial deterministic lookahead, providing algorithms with theoretical guarantees, when the agents are informed of future rewards or transitions before acting. While their focus is on core RL components like rewards and transitions, our work brings this idea to a new domain: cconomic docision-making under uncertainly, where the lookahead instead pertains to external environmental paramelers such as income.
Recent work by Merlis et al. )024); Merlis 2024
These studies situate our setting within broader space of lookahead models, distinguishing traditional RL (where future outcomes estimated) from settings like ours, where future information within the lookahead horizon is known exactly. Our proposed online planning algorithm builds on this refined lookahead structure and underpins the paper's main technical results.
Contributions. Overall, the main contributions of this work are:
Online Planning Algorithm with Deterministic Lookahead: We introduce an online plan- ning algorithm that models an agent's sequential consumption decisions under stochastic income realizations and varying degrees of deterministic future information. The algorithm recomputes consumption policy at each timestep based on newly revealed income and shock information. This dynamic re-planning framework accommodates rcal-time updates and simulates bounded lookahcad in environments with financial uncertainty.
We formally characterize the util- ity gap between agents with different lookahead horizons, showing that the expected cumulative utility increases monotonically with the size of the lookahead. Under reasonable assumptions (e.g.. concave utility functions and bounded shock distributions), derive lower bounds on this gap and demonstrate tightness of the bounds.
Thcoretical Characterization of Lookahead Utility Gaps:
Empirical Evaluation Under Realistic Constraints: We empirically evaluate the impact of lookahcad on cumulative utility through simulations that incorporate practical constraints such as income shocks and minimun subsistence (i.e., payments for basic needs like food and shelter). We explore scenarios in which agents differ in lookahead horizon and income volatility, evaluating the marginal value of lookahead information.
Temporal Effects of Information Asymmetry: We investigate how asymmetric access to future information leads to measurable differences in optimal decision-making trajectories, with a focus on how these effects particularly affect those representing socioeconomically disadvantaged groups.
Mitigation Strategies: We investigate mitigation strategies inspired by regulatory interventions such as fair workplace laws to examine how the adverse impacts of just-in-time scheduling on util- ity, can be reduced. Our experiments evaluate the effectiveness of these interventions within our framework, exploring how policy-driven constraints on scheduling influence worker well-being.
Note on Terminology. Before moving to the next sections, we briefly clarify point of terminology. While could refer to our approach as "online learning", it more closely resembles "planning", where actions are dynamically selected in response to evolving states, rather than the traditional machine learning notion of incrementally updating a model as new data arrives.
2 Related Work
Work Schedule Instability. The current focus of research primarily lies in the field of sociology, specifically
examining irregular work scheduling and its various repercussions. Unstable schedules cause income volatility
[Hannagan & Morduch 2015 Morduch & Siwicki 2017 Farrell & Greig 2016 Reserve 2016 Schneider &
Harknett 2017) and income volatility results in financial and life hardship (Bania & Leete 2006 Reserve
2016 Loete Banial 2010; McCarthy et al. 2018 Lambert et al., 2019). This encompasscs issues such as
burnout from precarious work schodules (Schneider & Harknett 2019a] Hawkinson et al.) 2023) and work-
family conflicts (Golden] 2015
Henly & Lambert 2014), particularly affecting parents with unpredictable
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just-in-time schedules. The impact also extends to areas like anxicty and child behavioral problems linked to parental work instability (Schneider & Harknett 2019b). Additionally, the field of Hluman-Computee Interaction (HCI) has also strived to study similar repercussions with a participatory outlook (Uhde et al. Wood 2021 Lee et al.) (021)). They investigate the necessity of worker participation in deciding schedules to ensure lairness (Uhde et al., 2020) and how to use elicitation methods to figure out worker preference models to assist in schedule management (Lee et al. 2021p.
2020
Further, statistical data shows a pronounced unfairness in advance notices for altering work timetables for underprivileged groups. Hourly workers, individuals with lower educational attainment, women of color, and specific service sectors are disproportionately affected (Schneider & Harknett, 2019b McCrate) 2018) with managerial discretion (Wood] 2018 Lambert 2008). These work schedules make it difficult to plan for the future (Shah et al. 2015 and difficulty in planning would result in disproportionate financial poverty and hardship (Gennetian & Shafir 2015). Along the same lines, there are some reports pointing to scheduling
software and planning algorithms as factor behind more unpredictable scheduling, particularly for low low-wage
workers in the service industry {Kantor 2014 Lancaster 2015 Griesbach el. al. 2019 Zhang et al. 2022).
For example, a New York Times article pointed out how some employees with algorithmic schedules rarely
learned their timetables more than three days before the start point of workweck (Kantor 2014 or how
pay reduction is correlated with sudden schedule changes and sales figures (Lgggins 2020).
Simulation. Simulation has been used in many social settings (Nokhiz 2024]. including fairness in lending
2019), college admissions (Hul (Liu et al.] 2018), resource allocation (Ensign et al.] 2018 Elzayn et al.
et al.; 2019 Kannan et al., 2019), financial analysis (Cristelli et al. 2011]. technology adoption (Klügl &
Kyvik Nordás, 2023).. studying supply chain shortages (Yongsatianchot et al.
2023). ; and simulations of global
crisis like the pandemic to minimize the spread of virus (Abe et al.] 2022). p.
To study the effects of advance
notice on individuals, we follow in the path of research by D'Amour et al. 2020). Zheng et al. (2020), and
Nokhiz et al. [2021 2024;
Nokhiz 2024h. which use simulation as a mechanism to study behaviors of agents
in systems.
Consumption Models. Consumption models fall within the broader category of discounted utility (DU) models that collectively contribute to our understanding of how individuals navigate decisions related to consumption and saving over time (Deaton et al.) 1992 Deaton 1989). These models involve individuals engaging in discounted consumption utility maximizalion, where they generally prefer immediate rewards over future rewards of the same size (Chabris et al. 2010). The preision-making process involves choices
regarding when to consume or save (Samuelson 1937). Several widely used intertemporal consumption
models include the permanent income hypothesis (PIH), the life-cycle model (Deaton et al., 1992 Friedman
2018 Parker 2010), and the neoclassical consumption model (Bütler) 2001). The income fluctuation problem (IFP) is also related consumption model with an infinite time horizon optimization with income uncertainty and an upper bound consumption (the upper bound hinders any consumption more than the amount of
assets individuals own, i.e., one cannot consume more than what they possess) (Ma et al. 2020
Sargent &
Stachurski 2014
Deaton 1989:
Den Haan 2010
Kuhn 2013 Rabault. 2002).
Online Learning in Investment. In investment, where high volatility and real-time data prevail, an online
model is needed to allocate investments across assets and maximize cumulative wealth through sequential optimizations. This application of online learning, known as online portfolio selection (Dochow) 2016 Xi
et al. 2023 Li & Hoil 2014 2018), is an algorithmic trading strategy that predicts future prices of risky assets using historical data. Online learning algorithms then optimize the portfolio with loss functions tailored to financial objectives, aiming for maximum wealth.
While investment models |Bayrkktar & Young 2012 Grandits 2015) have valuable components like modeling of uncertainty, they can only imperfectly model consumption. They focus on portfolio allocation between risky and risk-free assets rather than consumption decisions. Although individuals can adjust allocations to avoid financial ruin, this has no direct equivalent in everyday saving and spending choices. Moreover, investment. models do not impose consumption constraints.
Reinforcement Learning and Lookahead. The concept of lookahead is well-studied in reinforcement learning (RL), where it typically refers to planning over a fixed horizon H by considering the expected outcomes of action sequences within that horizon (Sikchi et al. 2022). In this setting, the agent optimizes
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policies by evaluating the expected cumulative reward over H future steps, relying known or learned model of environment dynamics (Moerland et al. 2020; Sikchi et al. 2022 Dalal et al. 2021 Efroni et al. 2018). Crucially, this lookahead involves estimating expected outcomes based on the stochastic dynamics of the environment. In contrast, our formulation of lookahcad assumes deterministic knowlodge of future environmental parameters, such as income shocks, within limited horizon, with stochastic uncertainty only beyond this horizon. Unlike the RL setting, where lookahcad explores expected consequences over states and actions, our model works directly with known future parameters over the lookahead horizon.
Recent work by Merlis et al. 2024 Merlis 2024) considers partially deterministic lookahead in RL settings, where agents have access to exact future information about rewards or state transitions before acting. These works analyze performance guarantees such as competitive ratios and regret bounds. However, their focus is on one-step lookahead with explicitly defined states and actions, and their lookahead applies to rewards or transitions. While related, our work differs in that we consider deterministic lookahead over varying horizon lengths, focusing specifically on agents' consumption decisions under stochastic income. Our lookahead on environmental parameters rather than rewards or transitions, and our goal is understand the behavioral effects of different lookahead horizons, rather than to optimize policies in a general RL framework. Therefore, our claims, framework, and methodological approach differ significantly from those of Merlis et al. (0024]
Merlis 2024g..
3 Determining Consumption and Savings: An Adaptive Planning Algorithm
A crucial component of a framework designed to investigate the significance of advance notice (future looka- head) involves creating model that captures consumption under lookahead while accommodating uncer- tainty specifically, how individuals, facing financial uncertainty, make decisions regarding the amount to consumee and save. Although various models attempl to represent consumption under uncertainly, they all fundamentally rely on the concept of discounted utility, which is the most common model in economics for understanding the interplay between consumption and savings. In a discounted utility model, the agent, at each time step, consumes a certain amount e and receives utility u(c) from some concave function u. The ob- jective is to devise a policy to determine a consumption value e in a way that maximizes the total discounted utility. After this brief introduction, we will formally articulate the specific cases we study, assumptions, and models in the following section ($3.1)
3.1
Our Models
In this section, we introduce the main models that we study in this work. We consider both deterministic and stochastic models that use a discount factor to compute the utility. We assume that time is discretized into integer steps, and let T be the effective overall job timeframe, i.c., the algorithm's time horizon. Let de, Cr, M/ be the assets, consumption, and income at time f, respectively. We also let R, denote the gain from assets (independent of the size of the assets), i.e., the appreciation/ prvreiiationddeprecaatio /depreciation rate of assets. Let u(.) (in our context, we employ u(c)- = ve which in the class of isoelastic utility functions that are commonly used in macroeconomics) be the utility. Let Dy be the income distribution and Da be the returns distribution.
In all the models, the goal of the algorithm to maximize the total utility. More formally, is to solve the following optimization problem:
I
max Σ
g (((e))
(1)
Co 1=1
subject to: a++1 = Re(as - c.) + y and 0 a S az
The constraint 0 < S a ensures that the worker consumes from the assets available to them. This constraint ensures the worker could consume without going to ruin. The model equation a+41 = shows how assets evolve over time given the consumption and income.
The offline or deterministic model. In the offline model, the income and return values yt, R₂ are known priori to the algorithm (as, of course, is the starting asset value, 01). This is the most common model
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considered in traditional economic theory, and the solution can be found using dynamic programming. The "states" in the dynamic programming correspond to the time step of interest and the total assets remaining.
The stochastic model. In the stochastic model, the income and return values are stochastic and they come from known distribution. In this case, an algorithm can optimize the modified objective:
max CL
g(t-1) B(u(ce)
(2)
The parameters and the constraints follow the same definitions as in the deterministic case, with the caveat being that yt. R4 are updated using the "realized" values (not their expectations). Note that this already an online algorithm: at every i, the algorithm computes the consumption value using the expected y, R for the future, but as the ye, R& values get updated, the algorithm changes its behavior.
Finally, to explore the effects of future information (lookahead), consider combination of the two models.
3.2 Online Consumption Algorithm with Lookahead
We finally consider model that has "limited determinism" controlled by the extent of lookahead, and the rest of the process is stochastic. Formally, at any time t, the algorithm knows the exact values of yt+s and Reti, for i = 1, .T, for some lookahead parameter - = Additionally, it knows the distribution of the parameters for later time steps. Once again, in contrast to offiine economic models, our online model finds an adaptive consumption policy that changes over time given the lookahead as more information arrives.
The algorithm itself a straightforward combination of the deterministic and stochastic cases. At each step, the algorithm computes:
maX
B'u(cr)+ +E
Σ Blu(ca) 1
where E is the expectation over the stochasticity in income and returns beyond the lookahead horizon.
Note that the algorithm incorporates new data (as well as lookahead information) as it arrives, which is why it is an online algorithm. For simplicity, we assume that a lookahead of 7 implies the agent aware of the exact return and income values for the next 7 time steps, and for the time steps beyond T, distributions of these parameters are known.
For this model, we define Algorithm This algorithm solves a stochastic dynamic programming (DP) at the start (in Line 2 where it populates the table V (of size * T where is placeholder for the size of the assets, with dynamic resizing as the bounds for the assets increase) with the maximum utility values for each asset and time point pair in the possible paths of the stochastic system. The algorithm uses backward induction over a discretized space using the known distributions of income and asscts to populate the value table, With this in hand, at time point i, the goal is to run deterministic DP in Line 4 using the precalculated table V and use that to calculate the optimal consumption at that time point t. This gives us online algorithm that yields new consumption at each time point f, based on the set of historical choices as well as the lookahead information available.
4 Theoretical Analysis
In this section, we establish few theoretical results on the consumption behavior and the "power of looka- head". We analyze the advantage that a worker privileged with lookahead, could attain comparod to an underprivileged worker without lookahead. Let Vt: aty Ct be the income, assets and consumption at time t. Let T be the timeframe of the job and u(c)= = vc be the utility gained from consuming
It is also interesting to consider further hybrid models; c.g., the algorithu has lookahead over St, but not over R.. This also realistic in practice since return rates are governed by the market while income lookahead can be controlled the employer. We do not consider such models in this work.
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Algorithm 1 Online consumption with lookahead
1: Let T be the lookahead, dg be the initial assets
2: Solve the following optimization problem and save the maximum utility for each a,t in table V where Vla, 4)
gives the utility of a, pair,
Σ (tru(cc) (=0
max
E
C
Te+1 Ra c2) + for all t (yt E Dy, R. E Dr for 1 (O.....TT)
3: for r 0 to T do
4: Solve the following oplimization problem to get & given a, using dynamic programming,
8 ((())) + V(a+tltn++++7
max
a++1 = Ri(ai - ci) + ye for all (y, RG exactly known for all E (nr + b...rt +7))
5: Set dr+1 [a ex) +
return The sequence of cıs at each time
Our first result shows that even in the very simple setting of B (no discount factor), and income Vi in the range [0, Y], the difference between the total utility of algorithms with k-step lookahead and without lookahead can be ((k-Y). This is truc not only of the algorithms we study, but any algorithm. This indicates that there are instances where a worker with lookahead privileges gains an edge over an underprivileged worker without lookahead, and the advantage grows linearly with the level of lookahead.
Theorem Consider two individuals, one with a lookahead of sleps and one with no lookahead. Let C1 .2...., CT be the consumption of the individual with lookahead & and 2ı, ,,,..,,22 2T be the consumption of the individual with no lookahead. There erist instances where all incomes in the range [0, Y1, such that
T
Σ
Va
Σ
Vzs 2(KVY)
(4)
While our lower bound result is strong for large values of k; it is not very strong for small values. This is partly because we want to emphasize that a gap that grows with k holds even with RG = 3 = 1.
We demonstrate that for any lookahead k, there exists an income distribution (dependent on k) such that the agent with lookahead achieves (lk)) advantage in utility the agent without lookahead. This dependence on & does not weaken the claim,
goal is merely to establish the existence of such instances.
Proof. As discussed above, we consider very simple setting: B 1, returns R, 1 for all t. Further we will assume that the individuals start with = 0 (no initial assets).
We consider the following input. Let Y be any parameter > 0. Let = Y for L k/2 and yr = x. for k/2 < t < where æ is a value uniformly sampled from [0, 1]. Note that both the individuals (the one with and without lookahcad) know this input distribution. For simplicity, we also assume that the total time horizon T equals & (this assumption can be easily removed by setting Yt = [1+=a y for all t > k). As a final simplification, since the incomes can all be scaled, we can assume that Y y= for the remainder of the proof.
First, consider the individual with lookahead. Note that they can see the value of x, and thus they can consume an amount (1+2) at every time step. This is feasible bocause the first h/2 stops have income y 1, 1tm and the assets remain above the consumption at all time steps. This yields total utility of k /
Now, consider an individual who does not have any lookahead. Intuitively, they cannot guess the value of x, and thus consuming 2 is infeasible. But note that the individual may use a complex (possibly randomized) algorithm that consumes non-uniformly and achieve high utility. We show that this not possible.
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The starting point of the proof is the classic minmax theorem of Yao (Motwani & Raghavan 2013 for given input distribution, an optimal algorithm for inputs drawn from this distribution, is deterministic algorithm. In other words, in order to prove our desired lower bound, it suffices to restrict ourselves to deterministic algorithms and prove a bound on the difference total utility, in expectation over the choice of x. For any delerministic algorithm, since in time sleps 1, 1...., (k/2), the algorithun only sees income of 1, the values consumption 21; 22,...; 2(/22) are all fixed. Let S = 21 + 22 +...t + 2(k/2)-
First, suppose it happens that
1+r x S- 2 2
> c. k,
(5)
for some parameter c. In this case, we will argue that E: Vzi is significantly smaller than k. k/ starting point is the following inequality about the strict concavity of the square root function:
1tz
The
Lemma 1. Let a E 11/2,1) be a constant, and let w E (0, 1). Then we have:
Ve S
V Va+
(w a) w a)² 2/a
(6)
The proof follows by a simple calculation.
Proof. We have:
1 (w a) w)
(w a)²
の Va (w 100-00 a) = (w (w-a) a) (vu+ Va 2/a 2Va(v va)²
(7)
2/a"
2 w + va)
The denominator is < 8, and thus by rearranging, the inequality follows.
Now, let us write 1t By assumption, we have that |21 + 22 + ... + 2x/2 aal > ck, and thus we have
Σ i
a al > ck.
(8)
Next, can use Lemma I to conclude that
Svaskva
E( (2 12--a) a) (2: a)2.
(9)
Now, since the consumption cannot be larger than the overall income (which is ka), the middle term on the RHS < 0. Thus, we have
Wv
(2 - a2 a)2
(10)
iSk
Next, by the Cauchy-Schwarde incquality and equation
g
2 Σ 2s - al
1 T
Σ (la-aa² a)²
Eh.
(11)
This shows that if the values z; chosen by the deterministic algorithm satisfy equation then the algorithm with no lookahead has total utility (2k) worse than an algorithm with lookahead.
Together, the above inequalities imply that E, Vzi S kvaa of
The final step is to prove that if & is chosen at random from (0, 1), the condition equation 5 holds with a constant probability for some c 0. Since S is fixed, the condition is equivalent to 125
1tz
2 2c.
Equivalently, |4 1- - x > 4c. For any fixed a, if x muar (0, 1) the probability that |a x| S 1/3 is clearly < 2/3. Thus, the condition above must. hold with e 1/12, with probability at least 1/3.
Therefore, we have that with probability 1/3, the no-lookahead algorithm is 2(k) worse than the algorithm with lookahead, and it can never be better. Thus the expected difference between the total utilities is also ((k). Yao's minmax theorem implies that this bound holds for any (possibly randomized) algorithm. L
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Theorem I shows that an algorithm with lookahead has a provable advantage an algorithm that knows only the distribution of the incomes, even in the simplest setting where the decay factor / = and the returns are all 1. Furthermore, the advantage grows linearly with the amount of lookahead. In particular, if an individual has infinite lookahead, they can have an advantage of ((T)..
Next, we show that when ==1 and R for all i, the lower bound from Theorem cannot be improved. Lemma 2. Suppose == and the return R. for all t. Let 11,32....:. yr be a sequence of income values with yt 2 0 for all t. Then if the consumption sequence of a k-lookahead algorithm is {ei, C2....,rrl, there episls no-lookahead algorithm whose total ulilily is vci+ + ve2
VCT-K-
In other words, the difference in the total utility (belween the k-lookahead and the no-lookahead algorithms) is simply vCT-k+1 + ..... + /er. In settings where all the are of magnitude (income)) this corresponds to O(k) times the square root of the income, which is the lower bound in Theorem
Proof. The proof is simple: a no-lookahead algorithm can mimic k-lookahead algorithm, but with a delay of k steps. We will call this the k-delay algorithm. Let CI, ,,,,,,,,,777 Cr be the consumption squence of the given k-lookahead algorithm. The k-delay algorithm is defined as follows,
For 1 T:
1. If S k, consume 0
2. Flse consume G--k
The total utility bound is casy to see. One only needs to check that the algorithm is feasible (i.c., it satisfies the condition that the total consumption until time t is bounded by the total income plus the assets until that time). This is easy to check because the algorithm consumes for the first & steps, while the income Ye 2 0. Since the decay factor 3 = 1, delay does not change the utility the algorithm receives.
Remark. We see that the proof relies on having 3 = we take into account factors such as inflation (c.g., == 0.95), then the "power of lookahead" can likely be made much more significant ? The agents with lookahead could potentially use the lookahead information anticipate future gains and consume more than the expected consumption and therefore gain significant advantage the agents without lookahead.
5 Experiments
While one might argue that all the proof setup (e.g., the lookahead case considered) is not fully realistic, it serves to build intuition, while the simulations are the parts that operate in more realistic enviromment.
That is, although our analysis relies on a set of simplifying assumptions and does not use fully realistic parameters, the primary objective was to gain insights into the relationship between lookahoad and utility. These insights are valuable for interpreting the empirical findings, which are based on more realistic settings. The specific choices of distributions and parameters made in the theory were ensure the problem remained analytically tractable.
Therefore, in this section, using our algorithm, we explore three different sets of experiments regarding the effects of lookahead, the parameters involved in lookahead under uncertain job timetables, and mitigation schemes.
5.1 Experiment Setup
We will first introduce the different elements in our experiment setup 3
Workers. Within our framework, agents represent employed individuals who earn weekly income, own assets, and decide whether to consume or save. We create an income distribution of 10,000 individuals using 2019 income data from the US Census Burcau's Annual ASEC survey of the Consumer Price Index (by
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the IPUMS Consumer Price Survey) (Flood et al., 2020 PK 2019-2020). In the first stage, we eliminate outliers from the income distribution to address challenges related to individuals with exceptionally high or low earnings, which can be challenging to compare due to significant scale differences. We identify outliers by employing the commonly-used inter-quartile range (IQR) proximity rule (Dekking et al. 2005). Subsequently, we calegorize individuals into four distinct income groups: low incomes ranging from $1.22 to $1125.49, low-middle incomes from $1125.49 to $2249.75, high-middle incomes from $2249.75 to $3374.02, and high incomes from $3374.02 to $4498.29. This classification is achieved by partitioning the overall income range into these four segments. To establish asset values, individuals are assigned the median population asset value of $123,840, derived from median percentile net worth data and median net worth by income percentile data from the Federal Reserve (of Governors of the Federal Reserve System 2019
Regarding IQR: To create a representative and analytically sound income distribution, we apply IQR method to remove extreme low and high income outliers. Income data is typically right-skewed (Benhabib & Bisin 2018), with a small fraction of individuals earning disproportionately high incomes. The IQR method is well-suited for this type of data, it is non-parameein and does nol rely on the assumption of normal distribution (Insights 2025 Hubert & Van der Veeken 2008 Whaley III 2005). Outliers are defined as values falling below (Q1-1.) x IQR) or above (Q3+ 1.5
1.5 x IQR), where IQR = Q3 Q1, effectively trimming the extreme ends while maintaining the core structure of the data. Please refer to Appendix $ A.2 for additional real-world explanations, citations, and reasonings behind IQR.
Minimum Subsistence. Furthermore, our simulation considers minimum subsistence, i.e., the constraint that the individuals must allocate funds for their minimum basic needs, such as food and shelter (Zhang
& Liu 2020 Zimmerman Carter 2003 Álvarez Peláez & Díaz 2005; Shin & Lim 2011 Shim & Shin 2014 Antony & Klarl 2019 Dwork & IIvento| 2018 MMiranda-Pintee et al.) 2023 2020 This consideration acknowledges the fundamental requirement for individuals to fulfill their basic necessities as part of the
decision-making process regarding consumption and utility maximization. The minimum subsistence values are derived from mean annual expenditures in 2019 from the Consumer Expenditure Surveys of the US Bu- reau Of Labor Statistics (of Labor Statistios) 2019), stratified based on income levels. In essence, individuals with similar income levels are obligated to cover equivalent amounts for their basic needs.
Shocks. Shocks, defined as alterations to an agent's financial state due to schedule instability, play a pivotal role in influencing decisions related to consumption and savings. Shocks can either positively or negatively impact income, such as sudden work-hour reductions or increases. Here, the magnitude of income shocks ranges from -0.4 to 0.4, with shocks occurring as (1 +) income, where r represents the shock value and the income represents the current value of income uniformly sampled from the income distribution. The shocks are generated from Bernoulli process, with the shock size parameter uniformly sampled from [-0.4, 0.4]. We set the probability of shocks to 0.4
According to the JPMorgan Chase Institute, income volatility remained relatively consistent from 2013 to 2018, with median households experiencing an average month-to-month income fluctuation of 36% (JPMor- gan Chase Institute 2016). However, the report highlights significant variation in volatility across houscholds and occupations, noting that income instability is both highly heterogeneous across families and inconsis- tent over time for the same houschold. The median standard deviation of income volatility is reported as 0.37. This variability is further reflected in specific job sectors Retail workers, for instance, often encounter erratic scheduling, leading to income fluctuations of up to 50% in certain months (CLASP) 2022) (and the corresponding carnings). Gig workers, such as rideshare and delivery drivers, also face carnings volatility due to inconsistent hours and changing platform demand, with monthly income shifts typically ranging from 3.4% to 14%, depending on market conditions and algorithmic factors (Insider) (024).. Considering these patterns, we construct a realistic/reassnabbee shock profile as mentioned earlier for the experiments in this section.
4 As an additional note, income not constant. It is sampled uniformly from given distribution. Agents additionally get shocks on top of income, where the shock probability set to 0.4.
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Please refer to Appendix A.2 for further real-world explanations, citations, and reasonings behind the adopted shock profile. Also, an extra set of experiments based on the exact shock profiles in (JPMorgan
Chase Institute 2016) are presented in Appendix B.5
Isolating the Impact of Lookahead and Other Parameters. At each time point (here, workweek). each worker within an income group shares identical observable features, like income, shocks stemming from unpredictable schedules, and returns asscts. The sole point of divergence among individuals within the same group is the exlent of lookahead they possess. This deliberate design choice aims to isolate the lemporal impact of lookahead on utility, eliminating other financial factors' interference. The overall job timeline spans 26 weeks, i.e., a 6-month job duration. The returns are sampled from uniformly from [0.9, 1.1] and with probability 0.1 there is an additive shock uniformly sampled from [-0.05, 0.05] on the return rates. The return rate ranges used here are grounded in empirical observations of typical historical asset performance of 5 years preceding 2020 across broad spectrum (Carlson 2021 Bank 2020).
The discounting factor 3 is set to the commonly-used value of 0.95. In economics, it is common to adopt standard, reasonable value for the discount factor, like 0.95 Paatnaik et al. 2022 Cooper & Willis 2014 4
Please refer to Appendix A.2 for additional real-workd explanations, citations, and reasonings behind the discount factor and return rates. Additional experiments with more granular real-world return rates and a set of different discount factors tailored to specific real-world use cases like unemployment and education can be found in Appendix B
Clarification on Simulation Parameters. For completeness, we reiterate that detailed explanations of all simulation parameters, along with their real-world empirical grounding, are provided in Appendix A.2
5.2 Future Lookahead: An Empirical Inquiry
This section aims to examine the utility acquired by individuals under varying levels of lookahead. Specif- ically, the experiment seeks to compare those with minimal (or no) information about the future, such as protected groups like hourly, part-time workers, and specific racial groups that typically receive limited or no advance notice, against other workers with more foresight. The experiment setup is as explained in $5.1 and the outcomes of this experiment are depicted in Figure
35
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Figure 1: The final utility gained for different levels of lookahead is illustrated for four distinct income classos, each comprising 27 individuals. Workers are of similar features, with variations solely based on the temporal aspect, i.e., the amount of lookahead in their work schedules. The z-axis depicts the lookahead value and the y-axis represents the total utility at the end of I steps. The two orange triangles are in place to highlight the difference in the level of lookahead needed for approaching the near-maximum utility maximmm utility utility close to that of a worker with full information at T26)) as the income levels change.
Analysis. The insights from Figure 1 can be summarized in four key points. 1) Firstly, workers with lower lookahead and minimal information about future instability experience significantly lower financial utility

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compared to those with higher lookahead. Unsurprisingly, individuals struggle to manage their finances effectively when confronted with unforeseen schedules. 2) Secondly, lookahead has positive impact overall. Workers with more lookahead can efficiently manage their finances, resulting in higher utility. 3) Thirdly, workers do not require full information about their work schedules in advance. Even beyond the midpoint lookahead (lookahead 13), workers can achieve a utility comparable to those with complete information about their schedules. 4) Lastly, higher income leads to greater utility, as individuals can consume without concerns. This evident from the consistent shift of the plots along the y-axis.
However, irrespective of income level, having more than the midpoint level of lookahead proves advantageous for individuals. Providing people with advance notice of their schedules can be reasonably implemented for the next 2-3 months of work without requiring employers to furnish complete information at the start of their tenure. Notably, for higher-incoma workers, less future information needed to approach the utility values of someone with complete information, as observed by the leftward movement of the orange triangles across all lookahead levels.
Robustness. Additionally, to evaluate the model'ss robustness and account for variability, we run the simulation using 20 different randomly generated seeds, while keeping the original parameter settings from $5.1 consistent across all runs. Figure illustrates the outcomes by showing the average values along with 95% confidence intervals as error bars, providing a mcasure of the reliability and consistency of the observed trends.
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The main simulation in 5.2 is carried out with the original parameters in 5.1 Results are for running the simulation for 20 different randomly generated seeds. The plot displays the mean value, and the error bars display a 95% confidence interval.
Figure 2:
Analysis. The key obscrvations align with the bullet points discussed for the initial figure. That is, workers with limited foresight face significantly lower financial utility compared those with greater lookahead, highlighting the positive impact of anticipating future schedules. While complete schedule information is not essential, having moderate foresight (e.g., lookahead of 17) yields utility close to that of full information. Additionally, higher income consistently leads to greater utility, as it allows for more flexible consumption, evident in the upward shift of utility levels across the plots. more detailed breakdown of these results can be found in Appendix A.1
5.3 Dynamics of Asset Appreciation and Depreciation
Our simulated space provides a comprehensive platform for delving into the intricacios of parameters within work scheduling. This exploration includes understanding the behavior of individuals with diminishing assets compared to those experiencing favorable returns on their savings.
Thus, this section's objective is investigate the impact of asset appreciation and depreciation, i.c., positive and negative return rates on workers' assets on decision-making across various levels of lookahead. This also serves examination of scenarios wherein the workers already at (dis)advantage in terms of assets.
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Assets depreciate when their value declines over time, inffuenced by factors like risky investments, fluctuating market conditions, tax obligations, possessions becoming obsolete, and wear and tear, seen in vehicles, buildings, and cash saved without earning interest. Conversely, asset appreciation occurs when individuals receive returns on their savings (Reader et al. 2022 or make profitable investments stocks, among other
lactors.
All experimental settings are similar to that of $ other than the return rates on assets. Here, we compare negative return rates in the range [0.75,0.95] to positive return rates in [1.05,1.25] (Carlson. 2020
2021
Bank
05.1
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60.1
57.
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(a) Negative return rate analysis
(b) Positive return rate analysis
Figure 3: Individuals with similar features but varying levels of lookahead under negative return rates ranging from 0.75 to 0.95 on their assets, as well as positive return rates between 1.05 and 1.25 on their assets.
Analysis. The findings are illustrated in Figure 3 Several insights emerge from this analysis: 1) Firstly, workers generally experience higher utility when they encounter favorable return rales. This is evident by comparing the utility range in the negative rates plot, which spans from 15 40, the positive plot, which ranges from 45 to 65. 2) Sccondly, with depreciating assets, individuals benefit significantly from small amounts of lookahead, reaching near-maxinun utility. People across income classes achieve near- maximum utility before Lookahead 10. There is a consistent decline in the lookahead value required to attain near-men marimax utility, reaching around lookahead 5 for the highest income class and around 10 for the lowest income class. This observation aligns with the trend observed the previous section, where more income classes require less future information to reach peak utility values. 3) Thirdly, the case of positive returns, individuals have more flexibility in consumption, as they anticipate overall favorable returns ahead. Future information is not crucial as in the negative returns scenario, where they are not at disadvantagcous situation with depreciating assets. This explains the late convergence of all income classes to the peak utility value (under positive return rates).
An additional set of experiments with more granular real-world return values is presented in Appendix B.4
5.4 Interventions
In this section, the goal is examine the mitigating effects of two intervention scenarios. In terms of inter- vention policics, simulation provides a valuable sandbox environment for testing that might be challenging even impossible to explore in the real world. In simulated work scheduling setting, researchers, pol- experiment with various interventions, assess their effects, and fine-tune
ieymakers, and practitioners strategies without real-world consequences.
All experimental settings are similar to $5.1 We assign interventions (to a sample of 50 individuals per intervention), as follows: (1) Compensation: Workers will be compensated for sudden schedule changes and on-call shifts. This policy modcled after the measures approved by the San Francisco Board of Supervisors, which introduced new protections for retail workers in the city, necessitating employers provide compensation for unpredietable schedules based factors such employment type, hourly rate,
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(a) Box plot of interventions
(b) Error bar plot of interventions
Figure 4: The box plot and the error bar plot of the statistical distribution of additional gained utilities for various interventions. The interventions considered are LO + Money, which involves compensation fees for individuals with no future information; L2, assigning at least two weeks of lookahead to all; and L5, assigning at least five weeks of lookahcad to everyone. In the box plot, the green triangle represents the mean, and the green line represents the median. In the error bar plot, the blue circle represents the mean and the error bars are 2 standard deviations from the mean (95% confidence interval).
hours of work (Golden 2015 Inspired by this policy, we disburse twice the amount of carnings back when there is negative shock. (2) Mandatory minimum advance notice: Every worker should be entitled to mandated minimum lookahead, i.e. they should be aware of their schedule for the upcoming two weeks. This proposition is inspired by the Schedules that. Work Act of 2014 (H.R. 5159) presented in Congress, which stipulates that there are alterations to the schedule and minimum hours, the employer must inform the employee at least. Iwo weeks prior to the start point of the new schedule (Golden 2015). Inspired by this policy, we assign workers two weeks and roughly one month (5 weeks) of minimum lookahead, separately.
Note that here the compensation setting is about adding fixed constant to income when there is shock. In these experiments, we did not explore multiple values, as the goal is to study the effects of giving realistic fixed amount of money.
Analysis. Results for intervention scenarios are depicted in Figure 4 as box plot to show the distribu- tions (and a separate corresponding error bar plot to capture uncertainty). Three insights can be derived: 1) Firstly, interventions have a positive impact overall, evident from the increased utility across all statistical metrics (mean, median, confidence interval, and all quartiles) post-intervention. 2) Secondly, while compen- sation the form of additional income for unanticipaled schedule changes beneficial, does not substitute for providing workers with advance notice of their shift schedules. Having knowledge of future plans with the same income but a prodictable schodule appears to be more effective for workers' financial well-being than an unforeseen, volatile schedule compensated with fees. A comparison between LO + Money and L2 indicates that even incorporating two weeks of lookahead is more advantageous than providing compensa- tion for instability without any lookahead. 3) Thirdly, offering just one month of advance notice results in a notable increase in utility, as seen in the comparison between L5 and LO. Even small amounts notice can significantly enhance utility.
Note on the Robustness of Experimental Parameters/Results. We discussed the results for 20 different randomly generated seeds (with 95% confidence interval) in Section $5.2 and have provided more detailed discussion in Appendix $A.1 It is important to mention that we conducted these experiments with various random seeds, considcring different runs (c.g,, with a median asset of approximately $70,000 (Aurelia Glass 2023). representing the median working-class wealth, as opposed to the population median), and with other realistic discount and return parameters, as well as varied plausible shock sizes. The overall trends in our results in the previous soctions remain consistent as long as the chosen parameters fall within more realistic ranges. If one opts for more extreme and unrealistic parameters, the distinctions observed in 5.2 5.3 and 5.4 may become more pronounced.
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Note on Additional Real-world Scenarios. As previously noted in several instances, to explore more diverse settings, we incorporate four additional case studies: the role of schedule instability during unem- ployment in B3.2 the influence of educational attainment on consumption behavior and patience for future information in $B.3 a more granular analysis of return rates by comparing cash and stocks in $B.4 and more diverse real-world shock profiles in [B.5 Across these diverse scenarios, we observe behavioral pal- terns consistent with those identified in the core sections. Further details can be found in the corresponding appendix sections.
6 Discussions and Limitations
The primary contribution of our paper lies in the development of an online framework that delves into the financial insecurity stemming from work schedule instability. This framework addresses two crucial ques- tions pertinent to work scheduling: 1) How can we develop an online planning approach for consumption under uncertainty to formally and empirically assess the negative effects of work schedule instability on crrome//mmplymmentte 2) How can this in turn help with informing the development of effective mitigation policies and regulations in the workplacc? We provide analytical insights into how lookahcad significantly enhances individuals' utility, with a focus on the effectiveness of increased lookahead. Our empirical investi- gation employs simulations and explores two distinct intervention strategies aimed at mitigating the adverse effects of schedule instability. While our model is being deployed in work setting, it applies to any scenario that involves temporal uncertainty with the possibility of improvement with lookahead. Our paper, however, has a number of limitations:
Simulation. A simulation is only as good as the models used to build and relics on idcalized and formal models of human behavior that are simplifications. A simplified model however is useful for an inquiry into limils: in our work, we show that even under ideal models of human ntility-maximiiing behavior, the lack of predictability and lookahead has concrete consequences for financial stability.
Homogeneity. The simulation assumes societal uniformity within income groups, considering temporal differences as the main variation. However, this overlooks other social inequities and heterogeneities that could impact decision-making (Nokhiz et al. 2025). Income instability can be influenced by factors such as gender (Blau & Kahn 2017), ability (Whittaker et al. 2019), race (Zwerling & Silver 1992). and health status (Hicken et al. 2014). Additionally, access to public policies addressing these disparities may also differ across demographic groups.
On Algorithmic Scheduling. In the digital age, algorithmic processes and digital technologies play a crucial role across various workforce sectors, from business process management to automated work schedul- ing. These tools enhance efficiency and productivity, offering advantages over manual scheduling methods by saving time and effort while providing greater control to managers and employees. However, despite these benefits, algorithmic scheduling can also introduce new challenges (Lancaster 2015).
Scheduling analytics have the potential enable operators to exploit their workforce unfairly. Reports factor behind more unpredictable scheduling
from The New York Times point to scheduling software practices, particularly for low-wage workers in the service industry (Lancaster] 2015). From the standpoint of employees, this uupredictability in scheduling is perceived as a negative attribute. It is an instability enforced by employers, often utilizing workforce management technology and algorithms. Therefore, it would be beneficial to enhance our modeling approach by incorporating more provisions to account for the intricate details and mechanisms of algorithmic scheduling parameters and operations.
Challenges in Data-Driven and Model-learning Approaches. While our simulation framework draws simplified models, this abstraction is intentional and grounded in well-established models in economics. These models allow us to examine the utility implications of lookahead and schedule instability in controlled setting, using parameters informed by real-world data. Nonetheless, we acknowledge that real-world financial behavior is shaped by additional layers of complexity (like social, behavioral, psychological, occupational, and so on). promising future direction involves integrating data-driven components such as using real-world behavioral data to learn parameters and the simulators or learning transition dynamics from observational datasets. However, such approaches face significant obstacles due to the lack of large-scale longitudinal
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datasets capturing individual consumption and income patterns at sufficient gramularity Furthermore, in social systems, the dynamics are not easily observable, complicating the application of typical model-learning approaches. As such, while learning simulators from data holds potential, our current simulation approach remains a feasible and interpretable tool for exploring the impact of work scheduling instability on financial planning behavior.
More Future Directions. Enhancing this framework could involve integrating additional financial factors linked to temporal uncertainty, such retirement savings constraints, differentiation between risky and riskless assets, and broader socioeconomic shifts like workplace restructuring or job relocations. Additionally, the framework offers opportunities to explore fairness and incquity in automated shift scheduling, particularly for sub-populations with sensitive attributes. It also enables research into targeted interventions within specific work environments (e.g., food and retail sectors) to mitigate the long-term effects of biased decision- making. Lastly, another additional direction for future work to employ empirical real-world data learn model parameters and simulate system dynamics based on observed behavioral patterns.
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A
More Experimental Details
This appendix section presents the robustness findings along with additional details on the simulation pa- rameters used.
A.1 Robustness
As mentioned in 5.2 we have included the robustness plot here well to provide more detailed analysis. That is, to check for robustness, we run the same original experiment mentioned in $5.2 as follows:
The experiment is conducted using the original set of parameters in $5.1 ensuring consistency across all trials. To account for variability and assess robustness, the model executed for 20 different randomly generated sceds. The resulting Figure _ provides a visualization of the data by displaying the mean value. The error bars included to depict the 95% confidence interval, offering insight into the robustness of the patterns shown before.
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Figure 5: The simulation in 5.2 is carried out with the original parameters in 5.1 Results are for running the simulation for 20 different randomly generated seeds. The plot displays the mean value, and the error bars display 95% confidence interval.
A Analysis. The insights from Figure are similar to the ones in 5.2
The results and consumption patterns observed before observed in this plot, which indicates robustness.
Workers with limited foresight and minimal knowledge of future schedule instability experience notably lower financial utility than those with greater lookahead.
Overall, lookahead has a positive effect: workers with more foresight can better navigate financial decisions, leading to higher utility.
Full knowledge of work schedules in advance is not necessary. Even beyond the midpoint threshold (lookahead 17), workers achieve utility level comparable to those with complete schedule informa- tion.
Higher income directly translates to greater utility, as individuals can consume without financial constraints. This is clearly reflected in the consistent upward shift of the plots along the y-axis.
A.2 More Clarifications on Simulation Parameters Used in $5.1
Why IQR and IQR Sctting. To ensure a representative and analytically robust income distribution, we remove extreme low and high income outliers using the Interquartile Range (IQR) method. Income data is characteristically right-skewed (Benhabib & Bisin 2018), with small number of individuals earning
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disproportionately high incomes. The IQR method is particularly well-suited for such data because it is non- non-parametric and does not assume a normal distribution, unlike z-score-based methods, which can be distorted by skewness (Insights 2025; Hubert & Van der Veeken 2008 Whaley 111, 2005 Specifically, per IQR's dcfinition, the outliers are values below (Q1 - 1.5 x IQR) or above (Q3 + 1.5 x IQR) where TQR = Q3 - Q1, effectively trimming only the extreme tails while preserving the integrity of the central distribution.
Shocks. The parameters chosen for modeling income shocks are grounded in empirical findings from real- world data. Since the shocks are very different household by household and occupation by occupation, the common practice in economics is to adopt a reasonable range.
According to the JPMorgan Chase Institute, income volatility remained fairly stable between 2013 and 2018, with households at the median experiencing a 36% change in income from month to month on average [JPMorgan Chase Institute 2016) (an additional set of experiments based on this shock profile in ( However, volatility levels vary substantially by household and occupation. The same report notes that income variability is highly hetcrogeneous, both across different families and over time for the same family. The median standard deviation of volatility is reported as 0.37.
Further illustrating this variability, retail workers often face unstable schedules that result in up to a 50% variation in work hours (and the corresponding carnings) during certain months (CLASP) 2022). Similarly, gig workers such as rideshare and delivery drivers experience changes in earnings tied to fluctuating hours and platform demand, with income shifts ranging from 3.4% to roughly 14% month-over-month depending on market conditions and app algorithms (Insider 2024).
Taking these observations into account and to have reasonable shock profile, opt for income shocks that ranges from -0.4 to 0.4, with shocks occurring as (1+r) x income, where represents the shock value. The shocks are generated from Bernoulli process, with the shock size parameter r uniformly sampled from [-0.4, 0.4].
Discounting Factor 3. Similarly, the common practice in economics is adopt a slandard, reasonable value for the discount factor, like 0.95 (Patnaik et al., 2022 Cooper & Willis 2014) [ However, a body of roscarch soeks to go beyond this uniform assumption by estimating more context-sensitive / values that vary across demographic groups. For example, as discussed in the following Sections [.1 B.2 and B.3 8 can change with education level or employment status. We provide detailed analysis of these more granular real-world scenarios in Appendix B
Return Rates. The return rate ranges used in $5.1 are grounded in empirical observations of typical
historical asset performance of 5 years preceding 2020 across a broad spectrum (Carlson 2021 Bank 2020).
As with most economic parameters, return rates can vary significantly depending on individual circumstances and the type of asset involved. We consider typical asset returns, not highly-volatile assets. For instance, if individual owns cryptocurrency and other very high-risk assets, they can have return rates like +215.07% or +539.96% during certain quarters and then experience very drastic drops in asset values!?
Therefore, like other parameters, the common practice is to choose a range that reflects realistic variability. However, as further examined in SB.4] a more granular analysis possible by focusing on specific typical asset classes (such as slocks or cash), which allows for a more precise assessment of return dynamics. Still, these specific return rates generally remain within the broader range defined in the initial simulation.
The description of range and the added variance of returns implics return rates uniformly distributed in given range. With probability 0.1, get an additive shock to the return rates where the additive amount is sampled from a different uniform distribution (Thus, 'a range and the added variance' is not about uniform + Normal additive returns).
htw.s//w.w...................oe. http:://www.coinggaa.t
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Discretization of the Dynamic Programming. In the simulations, the asset space is discretized into integral buckets with the gap between the buckets set to 1 where the number of buckets depends on the difference between highest attainable assets and the lowest possible assets (which could be non-zero depending on the income distribution).
Details of the Simulation Runs. The main results presented in $52 are based on a single set of sim- ulation runs for representative individuals within each income group and for 50 runs in the mitigation experiments. This choice was intentional, as our goal was to avoid averaging across agents, which can ob- scure meaningful behavioral variation, especially in a setting where individualllevel dynamics are interest. As discussed in the main text, the qualitative trends in consumption and utility remain consistent across different random seeds and repeated runs. However, to meaningfully support this, we include robustness (similar results, but further expanded in the
additional results across 20 random seeds in Figures and 2 respective appendix section), which confirm the stability of the main palterns.
In this context, the empirical findings serve as a complement to the theoretical results established earlier, helping to illustrate broader behavioral patterns rather than focusing on fino-grained empirical fluctuations. Given the heterogeneity of agents real-world socioeconomic environments, as shown in the detailed pa- rameter justifications above, our interest lies in capturing these general dynamics.
B More Real-world Problems
In this appendix, we explore additional scenarios informed by real-world data and observed phenomena.
B.1 Patience Factor based on B
In models of intertemporal choice, the parameter 3 denotes the subjective discount factor, capturing the extent to which individuals prefer present consumption over future consumption. A 3 value between 0 and indicates that future consumption is valued less than immediate consumption, with lower values reflecting a stronger preference for the present. This formulation closely aligned with the concept of present bias, which describes the tendency to overvalue immediate rewards relative to delayed ones.
A lower 3 implies greater impatience, signilying that individuals are more inclined to choose smaller, imme- diate rewards over larger, delayed alternatives. In contrast, higher values of 3 are associated with patience and a stronger orientation toward future utility.
Empiriaal studies on real-world events have documented that there are economic agents who exhibit more present-focused preferences, mcaning they are more prone to choose actions that yield immediate utility when those actions affect the present, compared to when all consequences are shifted into the future (Erieson & Laibson 2019 Lockwood 2020). In essence, these individuals make more impulsive decisions in the short term than they would if facing the same set of outcomes at future point in time.
The value of 8 plays a critical role in determining financial behaviors such as saving and borrowing. More impatient individuals (with lower 3) are typically more susceptible to accumulating debt, while those with higher & are more likely to delay gratification and engage in future-oriented behaviors like saving. In the following examples basod on real-worlh problems, we explore how these dynamics unfold in different contexts.
B.2 Unemployment
This section examines one of the most prevalent real-world problems: job insecurity and unemployment. We focus on how unemployed individuals experience varying levels of utility based on their capacity for lookahead, that is, their ability to anticipate future events. Specifically, the analysis compares unemployed agents who have minimal or no information about the future against those with greater foresight (and the related B).
Although this paper primarily addresses dynamic work scheduling, the underlying framework also applies directly to unemployed individuals, who typically face profound uncertainty. An unemployed person may not
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know: When whether they will find job, whether any job obtained will be full-time part-time, how long unemployment insurance (UT) benefits will last, whether they will experience unanticipated financial shocks during the job search, how partial employment affects UI eligibility and payments, and how and when to report carnings to maintain compliance with UI regulations.
Unemployment Insurance (UT) provides temporary income to eligible workers who lose their jobs through no fault of their own. However, UI exhaustion occurs once an individual has received all the benefits for which they eligible in given benefit year. At that point, no further payments are made unless the claim is renewed or the individual qualifies for extended benefits [Institution 2020 on Budget & Priorities 2021
The actual duration of UI varies significantly by individual and state, influenced by the following factors: UI is lypically calculated as percentage of previous wages, and individuals with higher earnings gel paid more. Also, most U.S. states allow up to 26 weeks of standard UI benefits. However, during economic downturns or recessions, extended benefits may become available (on Budget & Priorities 2021
Importantly, UT benefits generally employment, the rules are more nuanced. If the individual remains underemployed and continues to meet the cligibility requirements (typically related to carnings thresholds), they may still receive partial benefits. However, there is uncertainty on what can be categorized as an eligible partial employment and even if they are still eligible, UT payments may be proportionally reduced based on the income earned (Tne. 2021
when an individual finds full-time employment. For part-time
This complexity creates an environment where individuals make critical consumption and job search deci- sions under uncertainty. Prior work by (Lockwood] 2020 Ganong Noel 2019) provides empirical evidence consumption behavior during unemployment, revealing that the majority (approximately 75%) of unem- ployed households exhibit discount factor 3 = 0.9 which indicates more patience.
Thus, to explore this example, for our simulations, we use B = 0.9, following their setup. All other simulation parameters are similar to 5.1
30.0
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Figure 6: The final utility gained for different levels of lookahead is illustrated for the four classes, each comprising 27 unemployed individuals. Agents are of similar features, with variations solely based the temporal aspect, i.c., the amount of lookahcad in their future schodules. The r-axis depicts the lookahcad value and the y-axis represents the lotal utility al the end of T steps. Since agents are unemployed, we set 3 to be 0.9 based on the prior research [Lockwood
2020
Ganong & Noel 2019
Analysis Figure 0 illustrates the impact of foresight on utility for unemployed individuals across income levels. Three main insights emerge:
Individuals with little to no information about the future face significant utility losses. This is expected, as uncertainty in income, benefit eligibility, and job prospects limits their ability plan and allocate resources effectively.
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2. With increased foresight, individuals make better-informed financial decisions. The utility gain with more lookahead demonstrates that even in uncertain environments, information helps optimize consumption and savings strategies.
3. Hlighrreerning individuals consistently achieve greater utility, which aligns with their ability to consume without constraint. This result is evident from the upward shift in utility across the y-axis for the higher-earning group.
B.3 Real-world Educational-based Patience Factors
In this section, we examine another real-world scenario: the relationship between educational attainment, consumption behavior, and the benefits of having lookahead. While the previously used discount factor of 3 = 0.95 in 5 represents standard and commonly accepted value, our earlier analysis unemplyyment illustrates that patience can vary across different demographic groups. This motivates more context- sensitive exploration of B, particularly as it relates to educational background.
Prior empirical research demonstrates that individuals' time preferences reflected in their values are sys- tematically associated with their level of education. Specifically, individuals with high school diploma but college degree lend to exhibit more impatient behavior, corresponding to a lower | of approximately 0.50,
Conversely, those with a college degree tend to be more patient, with estimated 3 of 0.83 Laibson et al, 2024 Lockwood 2020). Therefore, in this simulation, we adopt 3 = 0.50 for workers with mid-level education and 3 0.83 for those with higher education, to better align our model with observed real-world behavior.
Except for this variation in values based on educational attainment, the experimental setup remains consistent with the bascline configuration described in $5.1 Figure presents the resulting utility outcomes for workers of varying education levels.
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(b) College degree lookahead analysis
Figure 7: The final utility gained for different levels of lookahead is illustrated for four income classes, each comprising 27 individuals. Workers are of similar features, with variations solely based on the temporal aspect, i.e, the amount of lookahead in their work schedules. The r-axis depicts the lookahead value, and the y-axis represents the total utility at the end T steps. Here, in the left plot, the income classes have a high school (i.c., mid-level) education level with 0.5 and they have higher oducation (i.c., college degroe) on the right plot with 0.83.
Analysis. The insights derived from Figure can be summarized through several key observations con- cerning workers with lower educational attainment:
Workers with lower education levels tend to exhibit higher levels of impatience. As a result, they reach their peak attainable utility more quickly than their more patient counterparts. For instance, individuals with only a high school oducation converge to their maximum utility within approxi- mately 5 weeks, whereas college-edueated workers continue to gain from lookahead information for up to 10 weeks.
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As observed in earlier settings, limited foresight leads significantly lower utility. Workers who lack access to future information or are unable to anticipate potential instability in their schedules are less able to optimize their consumption, resulting in diminished financial well-being.
Greater lookahead consistently improves utility outcomes. The ability to foresee and plan around future events allows workers to adjust their financial decisions accordingly (particularly within the first 5 weeks for high school-educated workers and the first 10 weeks for those with college degrees).
Higher income levels and higher education predictably lead higher utility even without lookahead. This is reflected in the difference in the range of the utility values along the y-axis in the two plots.
B.4 Real-world Return Rates on Liquid Assets
Similar to 5.3 this section's goal to investigate the impact of asset appreciation and depreciation on decision-matee makinng across various levels of lookahead, i.e., some workers are already at a (dis)advantage in terms of assots. While the return rates discussed in $5.3 are accurate when considering broad spectrum of assets and realistic return ranges {Carlson 2021 Bank 2020), can refine this analysis by focusing on specific categories, particularly liquid assets. Liquid assets refer to holdings that be readily converted into cash with minimal loss in value.
In this section, we examine two of the most commonly held liquid assets: cash and stocks. The primary distinction between them lies in their nature: stocks are investment vehicles that yield returns over time, whereas cash represents direct monetary holdings. Cash does not appreciate and is vulnerable to inflationary erosion but represents the most liquid form of asset ownership
To model realistic return variability,
empirical data from the five years preceding 2020 (i.c., 2016-2020)
Carlson 2021 Bank 2020). For stocks, set return range of 10%. For cash-only holdings, we assumee the individual is holding cash only, so based on real-world returns (Carlson All other experimental conditions are held similar to 5.3
2021
Bank 2020
we use -0.5%.
25
L15
120
Loak
Lockahbaad
midde
Low-rriads
(a) Stocks return rate analysis
(b) Cash return rate analysis
Figure Individuals with similar features but varying levels of lookahcad under various return rates. The return rates are set to 1.1 for stocks in the left, plot. In the right plot, the return rates set to 0.995 for cash. Other simulation parameters remain the same 5.1
The results, depicted in Figure are consistent with those found in noteworthy insights:
Analysis.
5.3 and offer several
Individuals achieve higher utility under favorable return conditions, like stocks. This trend under- scores the intuitive relationship between asset performance and consumption outcomes.
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Published in Transactions on Machine Learning Research (07 (025))
When holding very mildly depreciating asset such cash (only -0.5% depreciation), lookahead still boosts utility. Individuals quickly adapt their consumption in anticipation of diminishing purchasing power, Notably, since this asset is depreciating very mildly, the individuals attain near- mear-maximum utility later than the original negative return setting in $5.3 and by lookahoad 15.
In scenarios with anticipated positive returns (e.g., stocks), the knowledge of 10% increase helps individuals a lot in the beginning. However, after lookahead 5, individuals can afford to delay consumption, knowing they are likely to benefit from capital appreciation. As a result, convergence to peak utility occurs more gradually across all income groups (very late and around lookahead here), reflecting increased consumption flexibility.
B.5 More Real-world Shock Profile Case Studies
In this section, we examine another real-world scenario: the shock profiles based on the statistics provided by JPMorgaan Chase Institute (2016). According to the JPMorgan Chase Institute (as explained in $5.1
well as A.2 income volatility remained fairly stable between 2013 and 2018, with households at the median
experiencing 36% change in income from month to month on average (JPMorgan Chase Institute 2016 However, volatility levels vary substantially by household and occupation. The same report notes that the median standard deviation of volatility is 0.37.
Thus, we explore a case in which the shock value is selected uniformly at random from -0.36 to 0.36. We also consider the slandard devialion of volatility (i.e., coefficient of variation the ratio of the standard deviation to the mean), which is reported 0.37. This is done by the coefficient of variation being defined g where o² is the variance and is the mean. We set the coefficient of variance to 0.37, i.e., _ 0.37, which a
yields a 0.37p. In this case, we have μ 0.36.. We consider the values in the range of [4 20, μ 2 end up with -0.6264 and -0.0936 as the lower and upper bounds of the range from which shocks are uniformly sampled. All other parameters are similar to 5.1
25
110
L15
Loo-madde
low-rodde
High midke
hegh
(a) Shock profile analysis
(b) Shock with standard deviation of volatility analysis
Figure 9: Individuals with similar features but varying levels of lookahead under new shock profile. Shocks selected uniformly at random from -0.36 to 0.36 (left plot). We also consider the standard deviation of volatility, which is reported as 0.37 (right plot). Shocks are based on the exact statistics in (JPMorgan Chase Institute 2016). Other simulation parameters remain the same as 5.1
align closely with the findings discussed in $5.2 (since the shock profiles we originally opted for were based on realistic ranges similar to the ones listed in MMMggan Chase Institute 2016)):
Analysis.
The takeaways from Figure g
The same trends and consumption behaviors previously observed are present here well, reinforcing the robustness of our results.
Individuals with limited foresight and little knowledge about future scheduling uncertainty consis- tently experience lower financial utility compared to those with longer lookahead horizons.
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Published in Transactions on Machine Learning Research (07 (07/2025)
Greater lookahead generally leads to improved outcomes: individuals with more foresight are able to make more informed financial decisions, resulting in higher overall utility.
Having full foresight is not strictly necessary. Once the lookahead horizon reaches around 17 weeks, utility levels closely approach those achieved under full schedule awareness.
Increases in income correlate directly with higher utility, as they reduce financial constraints on consumption. This is clearly seen in the upward shift of the plots along the y-axis.
The standard deviation of volatility introduces fluctuations, particularly affecting the two lower- income classes, which are inherently more financially unstable. However, since the reported deviation does not indicate a siguificant variation, the overall trend remains unchanged.
The utility range for the deviation plot is of lower values compared to the left plot (since the shock range in the right plot mostly negative), resulting in an overall lower utility range (as reflected in the values along the y-axis).
30


Reviews:
[{"review_id": "vKZJqXPx8O", "reviewer": "Reviewer_qHqv", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "### Strengths\n\n- **Development of a Novel Online Learning Framework with Lookahead**: A core strength is the introduction of a novel online learning algorithm designed to handle varying levels of future lookahead. The framework's ability to model different lookahead levels makes it a powerful tool for systematically investigating how varying degrees of foresight influence financial decision-making in the context of unstable work schedules. The paper also provides some theoretical results establishing the advantage conferred by lookahead.\n- **Direct Relevance to Temporal Equity**: The paper effectively connects its technical framework to the pressing societal issue of temporal equity in workplace scheduling. This focus grounds the research in a critical real-world problem with significant social implications.\n- **Comprehensive Review of Related Work**: The paper provides a systematic review of the relevant literature. The authors effectively contextualize their work within the existing body of research, clearly articulating its position.\n- **Exploration and Evaluation of Mitigation Strategies**: The simulation framework is effectively used as a \"sandbox\" to explore and evaluate potential mitigation strategies for schedule instability. The analysis investigates interventions like compensation for changes and mandatory minimum advance notice periods.\n\n### Weaknesses\n\n**[Limited Scope of Analysis]**\n\n- One of the key contributions of this paper is its ability to provide analytical insights into lookahead through the proposed framework. However, both the theoretical analysis in Section 4 and the experimental analysis in Section 5 appear to be limited to specific cases and lack comprehensiveness, particularly in Section 4. For instance, the latter part of Section 4 discusses the case where $t=k/2$, but a more general treatment of this scenario would be beneficial. Given the simplicity of the theorem and lemma proofs, extending the analysis should be relatively straightforward.\n- Additionally, considerations beyond $\\beta=1$, $R=1$, or $y=1$ should be explored more broadly if feasible. Alternatively, if such limitations are common in prior research, explicitly acknowledging this would provide useful context. Similarly, Section 5 would benefit from more extensive numerical experiments or, at the very least, a clear rationale or precedent explaining the selection of parameter settings (e.g., how the shock generation aligns with real-world conditions).\n\n**[Validity of Assumptions]**\n\n- Related to the above, one of the key concerns is the lack of explicit justification for the fundamental assumptions underlying the proposed mathematical model. While assumptions are an essential component in modeling complex phenomena, their validity should be clearly motivated and supported by empirical evidence, theoretical foundations, or references to established literature. In the current presentation, it remains unclear why these specific assumptions were chosen. For instance, in Section 4, I feel that $x$ being uniformly sampled and each individual knowing this distribution seems like an unrealistic assumption. Without such clarifications, readers may find it difficult to assess the robustness and relevance of the proposed framework.\n\n**[Interpretation of Numerical Experiments]**\n\n- The lack of explanation regarding the numerical experiments makes it difficult to address several key questions. For instance, why does the total utility (y-axis) in Figures 1 and 2 not increase monotonically as the lookahead value (x-axis) increases? What is the number of trials conducted in each experiment? Are Figures 1 and 2 based on averaged results? How statistically significant are these findings?\n- Additionally, while the authors assert the robustness of experimental parameters and results, no clear evidence or simulation results are provided to substantiate this claim. Including such details would strengthen the validity of the conclusions drawn.\n\n**[Inconsistent Symbol Definitions]**\n\n- Throughout the paper, the same symbols appear to be defined differently in various sections, making it challenging for readers to follow the logic and mathematical formulations cohesively. For instance, the symbols for assets and consumption are denoted as $a_t$ and $c_t$ in Section 3, but are abruptly changed to $x_t$ and $z_t$ in Section 4. Even though the subscript $t$ has disappeared, $c$ and $x$ are also used with different meanings. $x\\sim_{\\text{uar}}(0,1)$ is probably undefined. To improve clarity and rigor, I recommend carefully reviewing all symbol definitions and ensuring uniformity throughout the paper. A consistent notation system will significantly enhance readability and prevent potential misinterpretations.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper investigates the impact of unpredictable work schedules on financial stability, particularly for vulnerable worker populations. The authors introduce an online learning simulation framework to model how workers adapt consumption strategies under uncertainty and demonstrate that foresight, or having a lookahead into future schedules, significantly improves workers' financial outcomes.\n\nAccording to the authors, key contributions are as follow:\n\n- **Online Learning Algorithm with Lookahead**: The paper introduces a novel online algorithm that handles varying levels of lookahead. This algorithm helps individuals use future schedule information to make real-time consumption decisions and adapt to financial shocks. It serves as a valuable tool for studying how different degrees of foresight affect decision-making.\n- **Formal Analysis of the Effects of Lookahead**: The study presents theoretical results concerning consumption behavior and the \"power of lookahead\". It is shown that workers who have lookahead benefit from an advantage that increases proportionally with the magnitude of their lookahead when compared to workers with no lookahead.\n- **Empirical Analysis of Future Information Provision**: The paper includes an empirical exploration of how future information aids in financial management and contributes to increased utility. Experiments using the online learning algorithm investigate the effects of lookahead under uncertain job timetables.\n- **Temporal Equity in Workplace Schedules**: The concept of temporal equity is explored, focusing on how the lack of advance notice (future lookahead) in work timetables acutely affects disadvantaged subpopulations.\n- **Mitigation Strategies**: The paper explores various mitigation strategies, referencing fair workplace laws and acts, to understand how the negative effects of just-in-time work schedules on workers' utility can be lessened.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "Based on TMLR's acceptance criteria, I have an overall favorable opinion of this paper. However, as noted in the Weaknesses section, I also have several concerns that need to be addressed. To ensure eventual acceptance, I would like to ask your views on these concerns, including appropriate revisions to the paper.", "broader_impact_concerns": "None", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "o1697x6IpH", "reviewer": "Reviewer_WcB1", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "**Strengths**: the submission is concerned with a real-world problem, and it motivates this problem via a variety of sources including academic literature, news sources, and government publications. This is unusual in machine learning publications and helps situate this potentially new domain. \n\n**Weaknesses**: I have both framing and technical concerns about the work. With respect to framing, the contribution does not \"read\" like a machine learning paper. Most of the prior work cited comes from the economic literature, the engagement with the ML literature (notably, RL) appears incorrect to me, and the notation is imprecise. With respect to the technical contributions, I find that I have to do a lot of guessing to infer what was actually done and what to make of it, the formal results seem overstated, and I'm not sure the analysis is fully correct or supported. \n\nI will expand on the core issues next. I did not go through for detailed minor comments and line edits as I think the paper needs a major rewrite at minimum which will likely change those minor details. \n\n## Motivation and prior work\n\n* Lookahead planning in ML usually implies taking an expectation over future states and returns given the current model. This is true both in e.g. H-step lookahead RL (as cited in the present contribution), lookahead in Bayesian optimization (e.g. https://arxiv.org/abs/1510.06299), and similarly in model-predictive control. By this definition, the stochastic model in section 3.1 already has \"infinite\" lookahead. The usual difficulty in this setting is having a good enough model for planning (in the current paper this would be a good estimate of $R_t$), plus efficiently managing the curse of dimensionality associated with taking the expectation over possible future realizations of states and actions. The submission claims in the related work section that \"the idea of H-step lookahead in RL is similar to the lookahead employed in our models\" but as noted above I think it's different in important ways. Furthermore, the claim \"our models operate with no explicitly defined states\" is also odd to me -- states are a sufficient statistic of history that decisions are conditioned on, i.e. the state is the current value of assets. \n\n* One recent line closer to the present contribution is work by Merlis and colleagues where an agent is provided with ground truth rewards (https://arxiv.org/pdf/2406.02258, https://arxiv.org/pdf/2403.11637). Here the term lookahead is used similarly to the present contribution (and note that one of the above papers considers the case where reward but not dynamics are given, as discussed in footnote 1). In this work, the idea that access to future states is beneficial is taken is a given, and the goal is to quantify the magnitude of benefit given the additional difficulty of computing this type of lookahead policies. That work is within the broader field of competitive analysis of online algorithms, where the goal is to investigate how well an algorithm which *doesn't* have access to the true realizations can do (https://csaws.cs.technion.ac.il/~rani/book.html). Also possibly related is work on the prophet inequality, which bounds how well an agent which knows distributions of values can do relative to an agent which knows the actual inputs (https://www.sigecom.org/exchanges/volume_17/1/CORREA.pdf). \n\n* Another related setting is in semi-autonomous agents which can query an oracle (usually a human) for some information about the evaluation environment (e.g. https://proceedings.mlr.press/v33/cohn14.pdf). Here the challenge is in determining what oracle information to obtain, and how to act if delay exists in query-answering. \n\nI'm not sure if all of the above work needs reviewing in the present contribution, but this is simply what I found from a few minutes of chasing potential connections. TMLR does not require novelty or significance, but for an ML audience to find interest in the contribution, it should be situated relative to other technical ML contributions. \n\n## Technical contributions\n\n* The overall presentation could be improved. For example, the equations in 3.1. should clarify what is being optimized w.r.t. to (e.g. $\\max_{c_t}$) since that is the controllable input. The notation switches from using $a_t$ for assets in section 3.1 to using $x_t$ starting in section 4. Figure 2 is given subfigures a and b but Fig 3 subfigures are unlabeled. Equations are numbered starting on page 7 but not earlier (even not earlier in Thm. 1). \n\n* Section 4 claims that the finding holds *even* without discount and without temporal discounting and asset appreciation / depreciation, and the remark after lemma 2 states that the proof relies on no discounting, and lookahead can be made more significant with discounting. I don't think this is supported -- the proof seems to rely on the fact that without discounting and no benefit / drawback to savings, one optimal policy is to always consume all the assets (I think in this setting and with finite horizon, any policy that consumes all the assets at any point is optimal). The lookahead agent can anticipate the next income and consume it immediately, and the no-lookahead agent needs to wait one step and then consume. Over a finite horizon, this means that the no-lookahead agent will lose out on the final step's utility because it cannot anticipate consuming the final income. Next, in the setup, the expected total income changes as a function of the amount of lookahead (since income before $k$ is $Y=1$ and income after $k$ is $x\\cdot Y$ where $x \\sim \\mathcal{U}(0,1)$). This artificially disadvantages the no-lookahead agent as lookahead increases, and seems like a weird setup at best (and at worst, is the source of the bound scaling with k). I haven't delved into the full proof in detail but this setup seems problematic. At the very least, the paper should moderate its claims and restrict them to the actual proof, provide better intuitions, and explain what's \"doing the work\" and what is a technicality. \n\n* It's not clear how the algorithm works. I imagine that the setup is something like finite-horizon backward induction over a discretized [time,assets] space. Next, in order to be able to compute the probability mass assigned to each cell, I imagine one would have to compute the CDFs of the income and return distributions. Is this correct? \n\n* The distributions of various terms are not made explicit. Section 5 describes a range and added variance of returns -- does this imply uniform + Normal additive returns? Or a truncated Normal? Section 5.1 additionally describes \"shocks\" with a magnitude that is a function of income and drawn from some distribution -- does this imply that income is otherwise a constant and drawn from the population for each simulation? What is the shock probability? \n\n* Section 5.4 describes L0+Money as compensating individuals for schedule changes and on-call shifts. Is this simply adding a fixed constant to income whenever a shock occurs as described in 5.1? What is the value added? How robust is the finding against different choices of this value, specifically given finding 2 in the Analysis paragraph of section 5.4 claiming that compensation for schedule changes is not as good as lookahead? I imagine this claim would only hold for some relationship between amount of compensation and amount of lookahead (e.g. if compensation on shocks is greater than the upper bound of income, then for every step where there is a shock, L0+money will outperform lookahead on that step, and if that benefit is greater than the benefit from knowing lookahead investment returns, L0+[enough money] should outperform any lookahead without compensation). To try to understand what was actually done I tried looking through the code but even though the files are ipynb, the simulations in them are minimally-documented C code so I did not dig very deeply. \n\n* No uncertainty is quantified for Figures 1 and 2 even though simulations are stochastic. Figure 1 claims that different income levels need different amounts of lookahead to achieve optimal utility but the difference looks numerically tiny (all lines basically saturate by L16 or so) and there are neither error bars nor hypothesis tests to support this finding. The same claim is made in section 5.3 and it is similarly unsupported. When uncertainty is quantified, it is not correct, e.g. the caption for Fig 3 describes the right side error bras as \"2 standard deviations from the mean (95% CI)\". It is true that for a known mean and variance, the *prediction interval* corresponds to approximately 2 standard deviations away from the mean. The CI is something about how well we know the mean (hence the CI for the mean given that the mean is known would be trivial), PI is something about a range within which future observations are likely to fall (hence if we know the mean and variance we can say something about what draws we might get). For the figures in the paper, the mean and variance are both estimated from the simulations, and we should probably be looking at the CI (which is a function of the sample variance, confidence level, and the number of observations) unless the number of simulations is large enough to shrink the CI to just be some small epsilon away from the mean. \n\n* The benefit of lookahead seems nonmonotonic in the amount of lookahead, notably in figures 1 and 2b. This is surprising (an agent with L5 can do at least as well as L4 by ignoring the information from step 5). I am assuming at least in Fig 1 this just noise is due to insufficiently many simulations ran, but especially in Fig 2b the pattern is the same across all income classes, which looks odd and makes me suspect a bug.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The submission proposes a model of utility maximization for an agent which can obtain the true values of the income and asset appreciation / depreciation over a fixed horizon. The motivation is modeling unpredictable work schedules associated with a class of jobs including gig work, food-service and retail, etc. The paper demonstrates theoretically that having access to this ground truth provides the agent with a benefit in a specific setting, and demonstrates a similar result by simulation in a more general case. Finally, it uses the model to simulate potential interventions including increasing lookahead and compensating workers for schedule changes.", "claims_and_evidence_yn": "No", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "See above, but most importantly: \n\n* The paper should clarify its engagement with other technical ML / stats contributions as relevant. At minimum I think this should include more correct engagement with H-step lookahead RL and the work by Merlis and colleagues cited above. \n\n* The proof claims should be moderated, and more intuition given on which claims are w.l.o.g., which are technicalities, and which are core to what's doing the work. \n\n* Missing detail in the simulation should be added (as discussed above) such that the work is properly reproducible. It's fine if some info is in supplementary material, but reading the code should be a last resort, not a requirement to understand things like distributions of various variables or discretization of the space for dynamic programming. \n\n* Claims w.r.t. simulations should be supported by statistical hypothesis testing unless so many simulations are performed that error is negligible.", "broader_impact_concerns": "I don't have specific ethical issues with the work that I want to call out. However, considering the work's motivation as it relates to a real set of problems in current work scheduling and financial instability, I think a broader impact section would be helpful to add. In some sense, a lot of the present motivation in section 1 could be a broader impact section, and the introduction could focus more on the technical aspects of the work.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "TtjMbj835Z", "reviewer": "Reviewer_6rip", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "**Strengths**\n\n* In general, well-written paper, good motivation and important problem to study\n* Real-world data based simulation across income and asset distributions provides interesting insights in real-world setup. Further analysis on intervention (which comes from real world governmental policy) make these results more interesting.\n\n**Weaknesses**\n\n* Some of the design are not well explained in the experiments (e.g. cut of IQR, plus many other choice of numbers in the simulation). A better way is to either provide some justification from the literatures or provide more diverse simulation experiments with various setup. I feel a well documented Appendix will be necessary. \n\n* Mapping real-world problems to experiments: I feel this paper could be strength by mapping real world problems to simulations choice (this is kind of related to the previous weakness).\n\n* Contribution of theoretical components: I am not sure how much contribute these proofs are, they seems to be somewhat obvious - can you map some of the theoretical results to the simulation?\n\n* Reinforcement Learning and Lookahead - this is the only technical related work section, could you expand this a bit more and maybe check some more recent papers?", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper studies the value of “lookahead”, an agent’s ability to anticipate future income shocks, in an online‐learning setting where agents face stochastic, last‐minute work‐schedule disruptions calibrated to U.S. micro-data. By varying each agent’s planning horizon, the authors demonstrate that even modest increases in foresight deliver substantial welfare gains (measured by end‐of‐horizon utility) and markedly reduce the probability of financial ruin. They then extend the framework to examine (i) how different lookahead depths interact with asset‐return volatility; and (ii) two policy interventions, pay compensation and mandatory advance‐notice mandates, showing how each can mitigate instability under realistic earnings‐shock scenarios.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "I would suggest the authors to go through my comments in the weakness section, and I think they should address everything, apart from mapping theoretical results to simulation in the next version (i.e. **Contribution of theoretical components**).", "broader_impact_concerns": "I need to put a note for the Action Editors that this particular topic falls somewhat outside my primary area of expertise; I hope my comments are taken more lightly.\n\nIn general, I think this is an interesting study with good impact for helping decision makers and policymakers invest more in helping especially working-class people build a financial risk forecasting mindset. This work seems to be of interest to the broader ML community.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)