Goal Recognition Design for General Behavioral Agents using Machine Learning
Authors: Robert Kasumba
Guanghui Yu
Chien-Ju Ho
Sarah Keren
William Yeoh
Venue: Accepted by TMLR ()

Abstract: Goal recognition design (GRD)  aims to make limited modifications to decision-making environments to make it easier to infer the goals of agents acting within those environments. Although various research efforts have been made in goal recognition design, existing approaches are computationally demanding and often assume that agents are (near-)optimal in their decision-making. To address these limitations, we leverage machine learning methods for goal recognition design that can both improve run-time efficiency and account for agents with general behavioral models. Following existing literature, we use worst-case distinctiveness (wcd) as a measure of the difficulty in inferring the goal of an agent in a decision-making environment. Our approach begins by training a machine learning model to predict the wcd for a given environment and the agent behavior model. We then propose a gradient-based optimization framework that accommodates various constraints to optimize decision-making environments for enhanced goal recognition. Through extensive simulations, we demonstrate that our approach outperforms existing methods in reducing wcd and enhances runtime efficiency. Moreover, our approach also adapts to settings in which existing approaches do not apply, such as those involving flexible budget constraints, more complex environments, and suboptimal agent behavior. Finally, we conducted human-subject experiments that demonstrate that our method creates environments that facilitate efficient goal recognition from human decision-makers.

Published in Transactions on Machine Learning Research (09/2025)
Goal Recognition Design for General Behavioral Agents us- ing Machine Learning
Robert Kasumba
rkasumba@uustt edu
Woshington University in Saint Louis
Guanghui Yu
guanghiiggn&uussst.ccom Cwwusttinmwwwwocccomc.m edu
Washington University in Saint Lowis
Chien-Ju Ho
chienjn.ho@@usstt..d
Washington University in Saint Louis
Sarah Keren
sarahk@essteccniion.co
Technion Israel Institate of Technology
William Yeoh
wyeoh& edu
Washington University in Saint Louis
Reviewed on OpenReview: https: // openreview. net/ pee//foree forum? id- GDuWBhoMNd
Abstract
Goal recognition design (GRD) aims make limited modifications to decision-males vironments to make it easier to infer the goals of agents acting within those environments. Although various research efforts have been made in goal recognition design, existing ap- proaches are computationally demanding and often assumee that agents are (ncar-Joptimal in their decision decision-making, To address these limitations, we leverage machine learning meth- ods for goal recognition design that can both improve run-time efficiency and account for agents with general behavioral models. Following existing literature, use worst-case distinctiveness (wed) decision-making environment. Our approach begins by training machine learning model to predict the wed for a given environment and the agent behavior model. We then pro- pose a gradientt-assd optimization framework that accommodates various constraints to optimize decision- makinn environments for enhanced goal recognition. Through extensive simulations, we demonstrate that our approach outperforms existing methods in reducing wed and enhances runtime efficiency. Moreover, our approach also adapts to settings in which existing approaches do not apply, such as those involving flexible budget constraints, more complex environments, and suboptimal agent behavior. Finally, conducted human- subject experiments that demonstrate that our method creates environments that facilitate efficient goal recognition from human decision-makers.
measure of the difficulty in inferring the goal of an agent in
1 Introduction
With the rapid advancement of artificial intelligence (AI), there has been surge in interest in human-Al collaboration, aiming to synergize human and AI capabilitics across various domains, such as gaming, commerce, healthcare, and workflow productivity. Designing Al agents to work alongside humans requires these agents to understand and infer human goals and intentions. While there has been abundant research in goal recognition (Ramírez Geffner, 2010; Sukthankar al., 2014), aiming observing their actions, this work focuses on the goal recognition design problem (Keren al., 2014), which seeks identify how to modify decision-making environments to make it easier to infer human goals.
infer human goals by

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Our work is built on the GRD problem formulated by Keren et al. (2014). They proposed the worst- case distinctiveness (wod) metrie, defined as the maximum number of decisions an agent can make without revealing its goal, to measure the difficulty of inferring the agent's goal. They then aimed to modify the decision-making environment, by removing allowable actions from states, to optimize this measure. Since the introduction of this work, there have been several follow-up works to deal with different settings, such as stochastic scttings (Wayllace et al., 2016; 2017) and partial observability (Keren et al., 2016). More discussion can be found in the survey by Keren et al. (2021).
While there has been significant progress in GRD, there are two main limitations in the literature. First, exist- ing approaches often assume that decision-making agents are optimal or near-optimal decision makers (Keren et al., 2015; Wayllace& & Yeoh, 2022). This assumption is unrealistic with human decision makers, who are known to often systematically deviate from optimal decision-makee due to cognitive and informational con- straints (Kahneman, 2003; O' O'Donoghue & Rabin, 1999). Second, existing approaches require evaluating the difficulty of goal recognition, i.c., worst-case distinctiveness (wed), for a large number of modifications to the environment. This computational requirement limits the scalability of these approaches, especially for virtual environments when there might be frequent updates of the environment, e.g.; e-commerce platforms might want to frequently adjust the website design to enhance user intent inference.
We propose a framework for GRD with general agent behavior to address these limitations. To relax the optimality assumption, we explicitly incorporate models of agent behavior into the optimization framework. To tackle the computational challenges, our approach leverages data-driven methods for goal recognition design. The core idea is to build a machine learning oracle that predicts the difficulty of goal recognition (e.g., wed) given decision-making environment and agent's is behavioral model. This oracle is trained datasets generated from simulations, enabling efficient evaluation of wed for any given environment and agent model. Such an approach significantly accelerates the evaluation process during optimization. Once the machine learning oracle is established, we apply a general gradient- based optimization method to minimize wed, using Lagrangian relaxation to handle constraints on environment modifications. Beyond addressing the two main limitations, this optimization procedure also supports more general forms of objectives and constraints that existing approaches in the literature cannot accommodate.
To evaluate framework, conducted series of simulations and human-subject experiments. We start with simulations in the standard setup in the literature, with the grid world environment and optimal agent assumption. show that our approach outperforms existing baselines in reducing worst-case distinctiveness (wed) and achieves considerably better run-time efficiency. We then conducted additional simulations to demonstrate that our approach can generalize to settings that existing methods cannot address, including scenarios involving flexible budget constraints, more complex environments, and suboptimal agent behavior. Lastly, we have conducted human-subject studies demonstrating that our method can be leveraged to design environments that facilitate efficient goal recognition from real-world human decision-makers. The results highlight the potential of our approach to enable more efficient human-Al collaboration.
Contributions. The main contributions of this work can be summarized as follows.
We propose data-driven optimization framework that accommodates general agent behavior and improves the efficiency of goal recognition design, addressing two main limitations in the existing literature while enabling a more flcxible optimization procodure. The framework consists of a predictive model that estimates the wed for a given enviroument and a model of agent behavior. We then apply a gradient- optimization method to perform goal recognition design. The framework is runtime efficient, capable of incorporating general agent behavior, and adaptable to different design spaces and constraints.
Through extensive simulations, we show that our framework not only outperforms existing approaches in goal recognition design, both in reducing worst-case distinctiveness wed and improving run-time efficiency in standard settings, but also adapts to scenarios that existing methods cannot handle, including general optimization criteria, complex environments, and suboptimal agent behavior.
Through human-subject experiments, decision-making agents are real-world humans. To the best of our knowledge, our work is the first to evaluate the encironment design for goal recognition with human-subject experiments.
demonstrate that our approach adapts to settings in which
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2
Related Work
Our work contributes to the field of human AI collaboration. Recent research shows that optimizing Al alone is insufficient to maximize the performance of human-AI teams (Bansal et al., 2021; Carroll et al., 2019; Yu et al., 2024), motivating efforts to understand and model human behavior in interactions with Al systems (Choudhury ct al., 2019; Shah et al., 2019; Kwon et al., 2020; Chan et al., 2021; Reddy et al., 2021; Narayanan et al., 2022a;b; 2023; Treiman et al., 2023; 2024; 2025). To build truly collaborative AT agents, they must also anticipate the intentions and goals of their human counterparts. This challenge lies at the core of goal recognition rescarch (Kautz, 1991; Ramírez & Geffner, 2010; Hong, 2001; Sukthankar et al., 2014; Percira et al., 2017; Masters al., 2021). Our work focuses on goal recognition design, an extension of goal recognition that incorporates environment modifications to make goals easier to recognize.
Goal recognition design (GRD) was formulated by Keren et al. (2014). Since this seminal work, numerous research efforts have extended to accommodate stochastic environments (Wayllace et al., 2017; Wayllace & Yeoh, 2022), varying levels of observability (Keren et al., 2016; Wayllace et al., 2020), and diverse design spaces (Mirsky et al., 2019). The studies most closely aligned with our approach focus on suboptimal agents (Keren et al., 2015; Wayllace Yeoh, 2022). However, these studies characterize suboptimality by limiting deviations from the optimal policy, a method that may not adequately capture the behavior of human agents, who frequently deviate systematically from optimal decision-making. Morcover, most existing work requires evaluating goal recognition difficulty at run time across a large number of environmental modifications, which significantly limits scalability. Our work distinguishes itself by broadening GRD to incorporate general models of agent behavior and by implementing a data-driven optimization approach.
There has been elfort lo accelerate GRD by using heuristic approaches that avoid the prohibitively large search space of possible modifications. In their seminal work, Keren et al. (2014) proposed the pruned-reduce method, which restricts modifications to action removal and leverages a key insight: blocking actions do not introduce new goal-directed paths. This alleviates the computational burden of exhaustive search. More recent work by Pozanco et al. (2024) accelerates GRD by using plan library from a top-quality planner (Katz et al., 2020) to guide initial heuristic exploration. Similarly, Au (2024) expanded the design space with block- level modifications simultaneous, intercomnected changes to improve efficiency. While these approaches make notable strides, they still rely on exhaustive search and repeated computation of complex metrics, which remains the primary computational bottleneck. In contrast, our method adopts a data-driven optimization framework. Rather than evaluating the metric (wed) at each step of the optimization process, we train predictive models to approximate it directly, enabling rapid evaluation and comparison of design candidates. Moreover, the differentiability of the predictive model allows for gradient-based optimization in place of exhaustive scarch. Together, these advances significantly reduce computational overhead and open new possibilities for scaling GRD to more complex settings.
Our methodology aligns with recent advances in data-driven optimization for mechanism design (Dütting et al., 2019; Golowich al., 2018; Curry et al., 2020; Kuo al., 2020; Rahme et al., 2020; Peri et al., 2021; Cornelisse al., 2022; Yu et al., 2023), which leverage machine learning to accelerate otherwise intractable tasks. It also aligns with recent research that incorporates human models into learning and optimization processes (Ho et al., 2016; Evans et al., 2016; Shah et al., 2019; Tang & Ho, 2019; 2021; Carroll et al., 2019; Tang et al., 2021a;b; Yu & Ho, 2022; Feng et al., 2024; Kasumba et al., 2025). While we share the high-level motivation, our problem formulation and methodological choices offer novel contributions and advance the study of goal recoguition design through a principled integration of predictive modeling and optimization.
3 Problem Formulation and Methods
3.1 Problem Setting
Decision-making enviromment. We define the decision decision-making environment as a Markov decision process (MDP), represented by W = (S, A, P. R). Here, S denotes the set of states, A represents the set of agent actions, P(s'|s,a) is the transition probability from state s to state s' upon taking action E A, and 8') represents the bounded reward received after taking action in state 8 and reaching state s'. To
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emphasize the goal recognition aspects of the problem, we introduce a set of goal states G S S. These goal states are terminal; that is, P(glg,a) = Vg E G,a A.
Models of behavioral agents. We represent the agent's decision-making policy in a general form IT 8 X + A. Specifically, for an agent with a decision- peeision-making policy π E II, the agent will execute the action t(s,t) in state s at time The agent is conceptualized as a planner H W + II, where the input is an environment w W, and the output is policy agent parameterized by time-variant discounting function d(t). The standard optimal agent model corresponds to fixed discounting factor 7 E [0, with d(() = 74. We can also represent an agent with present bias (O'Donoghue & Rabin, 1999) by adopting a hyperbolic discounting factor d(t) = 14kt' where k > O. Note that our approach not only accounts for standard analytical closed-form expression of agent behavior. It can also account for scenarios where an agent policy x is a machine learning model, i.c., a ncural network trained on human behavioral data.
II. To illustrate our formulation, consider
Worst-case distinctiveness (wed). To evaluate the difficulty of goal recognition, we follow the standard literature and focus worst-case distinctiveness (wed) (Keren et al., 2014), defined as the maximum number of steps an agent can take that are consistent with multiple goals before its truc goal becomes distinguishable. In other words, it measures the number of initial steps that overlap across trajectories toward different goals. To compute the wed for a given agent h E H in an environment w E W, we evaluate the path for the agent to each goal and compute the number of actions from the initial state that are identical for each goal. While we focus on wed in this work, our method is agnostic to the specific metric used, as long as the metric is computable, a predictive model can be trained to approximate it and enable efficient evaluation.
3.2 Goal Recognition Design (GRD) Formulation
We formalize the GRD problem with general behavioral agents. Given an environment w and an agent with a behavior model h, we denote the worst-case distinctiveness of environment w for agent as wod(w, h). Each type of modification 1 I i N will incur cost (ww, w²) that must fall in budget constraint B,. The objective of the GRD problem is to alter the environment from w to w' in way that minimizes work(w) w' h); while satisfying the constraint that the cost of the modifications does not excced the budget.
minimize w²
wcc(w', hh)
(1)
subject to c(w, S ViSI
3.3 Our Proposed Method
Existing approaches to GRD require ovaluating wed for a large number of potential environment modifications in order to identify the optimal ones. Since computing wed involves evaluating the agent's 's policy across multiple goals, introduces significant computational overhead and relies on strong assumptions about agent behavior. To address this challenge, propose leveraging machine learning to expedite runtime computation and explicitly account for general agent models. The main idea, illustrated in Figure 1, is to first train machine learning model that predicts wed for any given pair of decision-making environment w and agent behavioral model h. Once this predictive model is trained, we exploit its differentiability to develop an optimization framework that applies gradient- based methods to the Lagrangian relaxation of the constrained optimization problem defined in Equation 1. This approach not only addresses the two key limitation- computaiion challenges and restrictive assumptions about agent behavior- but also provides flexibility for accommodating various forms of optimization objectives and constraints.
Predictive model for wed. To build the predictive model for wed, we curate training dataset through simulations. For an environment w and agent behavioral model h, we can obtain wed(w, h) by solving for the agent's 's actions towards different goals. After collecting a training dataset, we train the prodictive model using a convolutional neural network. The implementation details are in Section 5.1.1 and the appendix.
Optimization procedure. After obtaining the predictive model, we develop a gradient- based optimization framework. This framework generalizes the existing literature in GRD where the space of modifications
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Agent Model
min Distance G)
Prediction Model
Raviromment
Ground Truth
Wcd
wed (wd()w
Updated w
Initial Environment
Prediction Model min Liwcd, wcd)
Converged
(wi
w
(wed Ac(w, w))
Proposed Approach
wod (W))
Proxy
(a) Predictive model for wed.
(b) Optimization framework.
We first train wed predictor from simulated data. We then perform gradient-based optimization that leverages the predictor to identify environment modifications that minimize wed with a given agent behavior model.
Figure 1:
is limited (e.g. usually limits to blocking an action in MDP) (Keren et al., 2021). The first step of the optimization procedure involves transforming the constrained optimization problem in equation into an unconstrained optimization problem using Lagrangian relaxation:
= wed(w' h)) +
Σ >c(a((ww w') B.).
We then perform gradient descent on the relaxed Lagrangian with respect to w. As environment modifications are often discrete (e.g., to block a cell in the grid world), we apply a discrete gradient descent procedure. Specifically, at each descent step, we obtain a gradient, which is a vector indicating the suggested change magnitude for each element (such as a cell in the grid world). We then select the element with the gradient value of the largest magnitude and make the corresponding change, Note that some suggested modifications may be invalid; for instance, cannot block already blocked cell in the grid world. In such cases, proceed to the element with the next highest gradient value, continuing this process until valid modification is made. This modification procedure is repeated until the gradient descent converges. Note that with this Lagrangian relaxation, while we cannot directly set the budget, based on duality, a larger Lagrangian multiplicr X corresponds to a smaller budget in the original constrained optimization formulation. practice, designer can choose vary the size of the Lagrangian multiplier modulate the budget. In our experiments, choose varying Lagrangian multipliers and record the realized costs of the modifications.
4 Experiment Setup
4.1 Benchmark Domains
We utilize benchmark domains. The first the standard basic grid world environment, commonly used in the GRD literature. The second is the Overcooked-AI environment (Carroll et al., 2019), more complex enviromment with richer set of environment modifications. This environment is particularly relevant to the downstream implications of our work, namely in supporting human-AT collaboration.
4.1.1 Benchmark Domain: Grid World
In the grid world domain, agents navigate grid with several potential goals. Consider an example in Figure 2a: an agent starts at point 'S' and aims for one of the goals marked 'G'. Spaces marked 'X' are blocked. In this example, the worst-case distinctiveness (wed) for an optimal agent is 0, as the shortest paths to the two goals do not overlap, meaning the agent's intended goal revealed on the very first move. Our experiments primarily focus on grid world environments with two goals for simplicity. However, our approach extends naturally settings with more than two goals by computing the relevant GRD metric and training a corresponding predictive oracle.
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G
X
X
X
X
X
X
S
X
X
G
X
X
(a) Grid world.
(b) Overcooked-AT.
Figure The benchmark environments. The left. one a grid world. The agent starts at a position marked and aims to reach one of the goal positions labeled 'G'. The agent must navigate through the grid, avoiding blocked cells marked with 'x. The right one an Overcooked-At setting, where the agent's 's objective pick up ingredients and complete their target recipe, which constitutes their goal.
Design space of environment modifications. In the context of GRD in grid world, the space of environment modification is often limited to adding blocks to spaces in the literature (Keren et al., 2014), also called action removal. In our work, we broaden the design space to also consider the unblocking of existing blocked spaces as potential modifications.
4.1.2 Benchmark Domain: Overcooked-Al
We also conduct our evaluations in more complex domain: Overcooked-AL This environment is based the popular game Overcooked, where players (agents) collaborate to prepare and deliver specific recipes. Since the goal of our approach is to enable efficient inference of agent goals, we focus on the simplified setting with a single agent. The environment is represented as a grid (sce Figure 2b), with cach cell indicating the object located there. Objects may include a counter, tomato, onion, pot, dish, serving point, or empty space. The agent can only occupy empty spaces and cannot step on any other object. It can carry movable items, Le., onions, tomatoes, and dishes, and place them on other non-space objects such as counters, serving points, pots. To navigate the environment, the agent move left, right, up, down and maintains orientation aligned with its most recent movement direction.
Goal recognition in Overcooked-AL. The agent's goal in Overcooked-A Al is defined by the recipe it needs to complete. For example, to prepare a soup with one onion and two tomatocs, the agent must collect the ingredients, place them a pot, and cook them. In the context of goal recognition, the objective to infer which recipe the agent pursuing based on its behavior. For simplicity, our experiments focus on scenarios with only two possible goals or recipes.
Design space of environment modifications. A primary challenge in the Overcooked-AT environment is its considerably larger design space for environment modifications. The design space includes changing the position of any object in the environment, subject to the constraint that the modification remains valid. This means that a change cannot result in a new environment design where any of the objects is unreachable by the agent. The objective of conducting experiments in this domain to assess whether our approach can address more complex domains.
4.2 Baselines
We compare our approach against four baselines that collectively represent the major algorithmic direc- tions in GRD: (Optimal) exhanstive search, heuristic-enhanced search, and greedy-based approaches. For heuristic-emhanced search, we implement the Fruned-Reduce method proposed by Keren et al. (2014) as a

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representative example. For greedy-based approaches, implement methods that use either the true predicted wed values to prioritize locally beneficial modifications.
Exhaustive search: This is the brute-force approach that evaluates wed for all the environments on the search path until the minimum possible wed is found. It is guaranteed to achieve minimum wod. However, given the computational overhead, this approach is not applicable in most situations.
Pruned-Reduce (Keren et al., 2014): This bascline is specifically designed for settings where modifica- tions are limited to action removal such as blocking a cell in grid world. It speeds up the exhaustive search and retains the optimal property. However, its scalability is still limited.
Greedy search using true wed: This greedy search baseline finds the single environment modification that leads to the maximum reduction of wed at cach itcration. This approach requires to evaluate the wed for all possible single environment modifications at each iteration.
Greedy search using predicted wed: In addition to greedy search using true wed, we leverage our predictive model for wed and design another greedy baseline. This baseline finds the single environment modification that leads to the maximum roduction of prodicted wed at cach itcration.
4.3 Models of Agent Behavior
In our experiments, demonstrate that our approach works for different models of agent behavior, We have examined three types of agent behavior.
Optimal agent behavior. The first one is the standard optimal agent behavior. Conducting experi- ments with optimal agent behavior enables us compare our approach with standard approaches in the literature, which are often developed under the optimal agent assumption.
Parameterized suboptimal agent behavior. We consider a generalized behavior model parameterized by d(t). The agent's objective is to optimize time discounted reward with the discounting factor for t steps in the future being d(t). The standard optimal agent model corresponds to fixed discounting factor ? E (0, 1] with d(t)= = = We can also represent an agent with present bias (O'Donoghue & Rabin, 1999) by adopting a hyperbolic discounting factor d(l) = I#k;; where k > 0.
Data-driven agent behavior. We also address settings where the model of agent behavior is a machine learning model trained on human behavioral data.
5
Experiments
5.1 Simulations
In our simulations, we first ovaluate how our approach compares with existing methods in standard sctups commonly found in the literature. We aim to show that our method matches or exceeds existing approaches in reducing wed while achieving significantly better time efficiency. We then demonstrate the generalizability of our approach by applying it to scenarios that state-of-the-art methods cannot address, including those with dynamic budget constraints, more complex environments, and suboptimal agent behavior.
Standard setting. We start with settings within the grid world domain, where modifications are limited to blocking cells and agent behavior is assumed to be optimal. This the standard setting for the majority of goal recognition design studics, as highlighted in Table 1 of the survey by Keren et al. (2021). The objective of this set of simulations to enable comparisons with state-of-the-ar methods.
In our experiments, the initial environment is generated randomly: we first randomly select the number of blocked cells from the range [0, 12), followed by randomly allocating the blocked cells. We also randomly determine the starting grid and two goal grids. Environments where the goals are nol reachable from the starting grid are filtered out. We randomly generate at least 500 environments and compare the average performance of our approach with that of bascline methods. More details of data generation and wed predictive model training are provided in Appendix A.1 and C. During optimization for our approach, the budget cannot be directly specified, we explored over range of Lagrangian parameters on a log scale
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between 0 and 10 (detailed in Appendix subsection B.2) and record the resulting realized budgets. We use the realized budget in our experimental figures because there is a monotonic relationship: larger Lagrangian parameters correspond to stricter penalties, generally producing lower realized budgets. This allows for a clearer comparison between methods that set budgets directly and our approach, which controls budgets indirectly through Lagrangian parameters.
We begin our experiments with 6
2.5
grid world. In this simplest setting, approach and all baselines achieve similar performance in reducing wed, as shown in Figure 3a. However, our method demon- strates a significant run-time advantage over exhaustive search. In particular, our approach requires only 0.2 seconds, com- pared to approximately seconds for haustive search.
2.0
wcd reduction
Exhaustive
Greedy (predicted wod)
1.0
Greedy (true wcd)
Greedy (predicted wcd)
0.5
Pruned Reduce
Prudud-Reduce
Greedy (true wcd)
Our approach
Our approach
0.0
5
10 budget
15
10
20 budget
30
40
(a) 6 x grids
(b) 13 x 13 grids
We then scale up the environment to a 13 x 13 grid, where both exhaustive search and the Pruned-Reduce method lailed to complete within an hour for single instance and were therefore ex- cluded from the baselines. As shown in Figure 3b, our approach outperforms the greedy baselines in reducing wed, due to its budget-aware opti- mization procedure that systematically accounts for the long-term impact of each modification modification-malliee making it less prone to shortsighted or myopic decisions. Additionally, our method is approximately three times faster than the greedy basclines for large budgets (with further runtime comparisons discussed later).
Figure 3: wed reduction in a grid world when only blocking modifi cations allowed. Exhaustive search and Pruned-Reduce not included in (b) because they take more than an hour to compute for a single environment.
Flexible budget constraints. In the literalure, most works focus on a single type of environment modification (e.g..
10-
wed reduction
8
wcd reduction
blocking cell). Given the flexibility of our optimization framework, we ex- tend our approach to include 'unblocking' blocked cells as a possible environment update. In our simulations, we exam- ine two common cases. In "shared bud- get", the total number of blocking and unblocking actions is bounded by a given shared budget. In "individual budget", we limit the number of blocking and un- blocking actions separately. Specifically, we allow the number of blocking actions be 5 times the number of unblocking actions (rounded to the nearest integer). Given that there are no established basclines (Pruned-FF) Reduce is limited to blocking only modifications, and Exhaustive Scarch does not scale) for this setting in the literalure, compare results against greedy baselines.
6
Greedy (predicted wod)
4-
Greedy (predicted wcd)
Greedy (true wcd)
Greedy (true wcd)
2-
Our approach
Our approach
1b
2b budget
30
40
10
20 budget
30
40
(a) Shared budget
(b) Individual budget
Figure 4: wed reduction in settings with two types modifications. We only included greedy the Mate-of-theears baselines Exhaustive search and Pruned-Reduce are not applicable in these settings.
The results are shown in Figure 4. Overall, they demonstrate that our approach is effective at reducing wed even when existing stato-of-tho-art methods are not applicable. addition, our gradient-based optimization outperforms the greedy approach except for small-budget cases?. This is because our method considers how to distribute the budget over time, rather than selecting the highest-impact modification at each step without considering future opportunities.
"Nte that definition of greedy approaches, the greedy approach using the true wed optimal when the budget since only one modification be made. As result, greedy methods generally perform well when the budget very small, but our approach outperform greedy with larger budgets.
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Complex domain and suboptimal agent behavior. We consider two additional extensions, where existing approaches in the literature do not apply, to demonstrate the flexibility of our framework. In the first, we evaluate our approach in more complex problem domain: Overcooked-Ar Al. In the second, we return to the grid world but include scenarios with suboptimal agent behavior. Both extensions utilize a grid size of For the Overcooked-AT environment, we assume optimal agent behavior and aim to explore how our approach adapts
much richer space of environment modifications. For the suboptimal human behavior, we employ the model described in Section 4.3, utilizing hyperbolic discounting factor d(t) I+kz and set k 8. For both extensions, standard approaches such exhaustive search and Prune- Reduce are either too slow or not applicable. Therefore, we compare our results with the greedy baselines.
The results for both extensions, as illus- trated in Figures 5a and 5b, demonstrate that our approach adapts well both settings. Our approach demonstrates a more significant advantage over baselines in Overcooked-Ar All than in grid world set- tings. The increased complexity and larger modification space in Overcooked- AT cause greedy methods to converge to short-sighted solutions, underscoring the superior scalability of our method. Re- garding runtime, our approach is again several orders of magnitude faster than the greedy method with true wed and at least 3 times faster than the greedy method using predicted wed.
5-
3.5
wcd reduction
wed reduction
2.5
Greedy (predicted wcd)
Greedy (predicted
Greedy (true wcd)
2.0-
Greedy (true wcd)
1-
Our approach
Our approach
1.5
10 budget
15
20
20
budget
(a) Overcooked-Al
(b) suboptimal agent.
Figure 5: Performance in other settings: (a) Overcooked-AI environ-
ment with optimal agent behavior, and (b) Grid world (6 6) with suboptimal agent behavior, demonstrating the method's adaptability to non-optimal decision-making
Running time comparisons. We have demonstrated that our approach achieves greater wed reductions compared to all baselines. Another key benefit of our method is its significantly improved runtime efficiency relative to standard approaches. This efficiency comes from (1) using machine learning oracle to predict wed instead of evaluating the true wed at each time step, and (2) applying gradient-based optimization rather than the (heuristic-enhaneed) exhaustive scarch methods used in the literature. As shown in our earlier sinulations, exhaustive search methods scale poorly. In the 13x13 environment, a single instance of GRD takes more than one hour, while our approach completes in about one second. Therefore, we focus on the improvements due the ML oracle in the following comparisons.
Table 1: Time (seconds) comparisons when using true wed and predicted wed. denoles standard
True wed
Predicted wed our approach
Setting
greedy
greedy
Standard (small)
0.11+0.01
0.47+0.0
0.5=0.0
Standard (large)
4.95++0.99
2.46+0.49
1.11+0.11
Suboptimal behavior
18311
0.5910.02
0.71
Complex domain
531:11
0.41
0.8
Table shows the time required to make modifications under a fixed budget across different settings. The results indicate our methods are generally faster and scale better in complex environments. For instance, in the complex domain, computing the true wed takes 531 seconds for GRD, whereas our approach takes less than 1 second. Additional discussion on the time improvements provided in Appendix A.2.
5.1.1 Ablation Study
We conducted an ablation study better understand the specific contributions of our proposed approach goal recognition design (GRD), particularly its ability to reduce wed. The study isolates two key components

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of our method: the accuracy of the predictive model used to estimate wed and the effectiveness of the optimization procedure in modifying the environment to improve goal recognition.
We evaluated several predictive models trained to estimate wed and tested them in combination with different optimization strategies. These are compared against baseline that applies a greedy search using the true wod without relying on predictive model. All experiments were conducted under three environment modification settings: the standard setting and two variants with flexible budget constraints (individual and shared budgets). Results for environments with grid size 13 are shown in Table 2, with additional results for grid size 6 provided in the appendix.
Impact of predictive model choice. We trained several predictive models, including Convolutional Neural Networks (CNNs), lincar models, and Transformers, using the Adam optimizer (Kingma & Ba, 2015) and selected the configurations through validation. CNNs consistently achieved the lowest prediction error, and crucially, enabled more effective environment modifications when combined with either greedy or gradient- based optimization. By contrast, linear models and Transformers performed worse in predicting wed and led to less effective downstream performance. This highlights the importance of predictive accuracy, where the quality of the predicted wod directly influences the success of environment design.
Impact of optimization approach. We also analyzed the role of the optimization procedure given a fixed predictive model, using (i) greedy optimization using predicted wed, and (ii) our proposed gradient- based optimization approach. Greedy optimization using predicted wed can offer runtime benefits over using true wed, but its effectiveness varies with prediction quality. In cases where the predictor was less accurate, the greedy method often failed to produce significant improvements in wed. Our proposed gradient-based approach consistently improved upon the greedy method. In particular, when combined with the most accurate CNN predictor (100K samples at learning rate of 0.001), our method achieved the lowest wed across all three modification settings, significantly beating the greedy baseline using true wed as well.
The best-performing configuration, CNN (100K, 0.001) combined with our gradient-based optimization, achieved the greatest reduction in wed and outperformed all baseline approaches. This supports our core claim: accurate prediction of wed paired with an effective optimization strategy, as adopted in our approach, is critical to designing environments that enhance goal recognition.
Table 2: Ablation results showing the impact of different predictive models and optimization methods on wed reduc- tion across three environment settings as described in subsection 5.1. Fach row represents predictive model trained with specified dataset size, learning rate, and associated training/validation loss. Due to poor performance, only the best Linear and Transformer configurations Greedy using predicted wed and our proposed approach, along with a baseline using greedy with true wed. Bolded results indicate the best performance per setting. Results are for grid size 13; grid size 6 results are in Appendix B.3
shown. For each model, compare two optimization methods:
Predictive Model
Loss (mse)
Optimization Approach
wed Reduction
Train Validation
Standard Individual
Shared
Baseline (NA)
NA
NA
Greedy (true wed)
7.6+0.4
9.2+:0.4
9.8+00.4
Greedy (predicted wed)
1.9.0.3
1.2.0.2
1.210.2
Linear (100K, 0.1)
14
15
Our Approach
2.1+0.22
4.8+0.33
5.4+0.3
Greedy (predicted wed)
0.0:0.00
0.1:0.11
00.600.11
Transformer (100K, 0.1)
20
20
Our Approach
1.5+0.2
4.2+0.22
4.5+0.3
Greedy (predicted wed)
1.9:0.2
0.840.2
1.0:0.2
CNN (IK, 0.001)
0.6
13
Our Approach
1.9+0.2
3.9+0.3
4.0+0..3
Greedy (predicted wed)
4.340.3
3.840.3
4.110.3
CNN (10K, 0.001)
0.2
4
Our Approsch
5.1+0..3
8.5+0.3
9.3+0..3
Greedy (predicted wed) Our Approach
7.140.4
8.9+0.3
9.8+0.3
CNN (100K, 0.001)
0.1
0.2
8.6+:0.4
10.4=0.3
10.8+0.3
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5.2 World Human-Subject Experiments
In our simulations, we demonstrate that our approach consistently outperforms baseline methods terms of wed reduction and offers greater efficioncy in runtime. To assess the applicability our approach when humans are the decision-makers, we conducted two sets of human-subject experiments. In the first, we aim to collect human behavioral data in our maaiiinnmmaking environments. Utilizing this data, we employ imitation learning to develop a model that accurately represents human behavior. This model is then integrated the agent behavior model within our approach. In our second experiment, we aim to evaluale whether our approach indeed leads to environments that facilitate more effective goal recognition by human decision- makers. These experiments are approved by the Institutional Review Board (IRB) of our institution.
5.2.1 Experiment 1: Collection of Human Behavioral Data
We recruited 200 Amazon Mechanical Turk workers, paying each $1.00 for an average task time of 3.64 minutes, equivalent to an hourly rate of about $16. Each participant is asked to play 15 navigation games in a 6 x 6 grid world, navigating from a start position to designated goal in each game. At each time step, they could choose to move in one of four dircctions: Up, Down, Right, or Left. A game concluded when the participant reached the goal. The enviromments for these games were generated similarly to our simulations, with start positions, goal positions, and block positions all being randomly determined. Our objective with this setup was to leverage the collected data to develop data-driven model of human behavior.
Learning models of human bchavior. The collected human data were split into training (160 workers, 70,000 user decisions), validation, and testing sets (20 workers, 8,800 decisions each). A 4-layer Multilayer Perceptron (MLP) was trained, with the environment layout as input to predict the next. human action. We fine-tuned hyperparameters and chose the model architecture using validation. We compared the performance of our Iearned model against one that assumes optimal agent bchavior i.c., taking the shortest path to the goal. Table 3 presents both models' accuracies, showing that human behavior significantly deviates from optimality. This deviation underscores the importance of incorporating realistic model of human behavior in GRD, particularly when humans are the mecision-makers.
Table 3: Prediction accuracy human behavior assuming optimal behavior versus using a data-driven model.
Model
Train
Val.
Test
Assuming optimal behavior
0.7266
0.6964
0.7131
Data-driven model
0.9189
0.8136
0.8422
5.2.2 Experiment 2: Evaluating Goal Recognition Design
We next evaluate our approach that incorporates the data-driven model of human behavior from Exper- iment 1. We randomly generate 30 initial enviromments using the same setup as in simulations. These environments are then updated according to four different methods, all operating within a modification budget of 20.
Original: No updates to the environment.
Greedy: Greedy baseline using predicted wed from the data-driven human behavior model.
Proposed (opt-bhvr): Our proposed approach when assuming the agent is following optimal behavior (i.e., picking one of the shortest paths towards the goal).
Proposed (data-driven): Our proposed approach using predicted wed from the data-driven model.
We recruited 200 workers from Amazon Mechanical Turk. Each worker was randomly assigned to one of the four treatments above, with the distinction between treatments being the environments presented to them. Workers were randomly assigned goal for each environment and tasked with navigating to reach it. We utilize the collected data to evaluate GRD design approaches.
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Comparing empirical overlapping
actions. To evaluate the elfectiveness of each GRD approach, we first mea- sure the empirical overlapping actions toward each of the two goals. Specifi- cally, each recruited worker is exposed to all 30 environments in their assigned treatment and is instructed to reach one of two randomly selected goals. For each treatment, we compute the num- ber of overlapping actions for every pair of workers assigned to different goals within the same environment. This yields a distribution of overlapping ac- tions for each treatment. This met- ric reflects the difficulty of inferring an agent's goal and serves as an empirical proxy for wed. Figure 6a presents the percentiles of the number of overlapping actions across treatments. Notably, in the lowest 25%, environments generated by our approach show no overlapping actions, indicating that goal inference is relatively easy in these settings. Overall, when combined with data-driven models, our approach produces environments with statistically significantly fewer overlapping actions (paired t-test, p-value 0.005); thereby facilitating more accurate identification of human goals.
# of oa actions
Original
Original
5-
Greedy
100-
Greedy
Proposed(ept-bhwr)
Accuracy(%)
proposeddopt-bhvee
Proposedidata
Propose d'data driven)
80-
60-
50-
0-25
25.50
50-75 Percentile
75-100
10
30
50
70
90
% observed actions
(a) Empirical overlapping actions (the lower the better).
(b) Bayeslan goal inference (the
higher the better).
Figure Comparing different GRD approaches in our human subject experiments. Our approach coupled with data-driven models is shown to generate environments that enable the most effective goal recognition with real human decision-makers.
Comparing the accuracy of goal inference. Instead of evaluating the effectiveness of our approaches based on wed or its proxy, we next directly assess whether human goals can be accurately inferred from partial observations of their actions. To do this, we use an off of--thesheef Bayesian inference algorithm (Murphy, 2012) 3, As the agent acts, we update the posterior belief using the likelihood derived from our data-driven bchavior model. Specifically, for cach worker, we reveal the first & portion of their actions to the inference algorithm, which then attempts to infer the worker's goal. This allows us lo compute the average inference accuracy. The results, shown in Figure 6b, demonstrate that our approach produces environments that make goal recognition easier.
6 Conclusion and Future Work
Effective human-Al Al collaboration hinges on the AI system's ability to infer human goals. In this work, we introduce a data-driven framework for goal recognition design (GRD) that optimizes environments to enhance goal disambiguation. Our method addresses two major limitations of prior approaches: computational inefficiency and the unrealistic assumption of fully optimal agent behavior. At the core of our framework is a learned oracle that predicts goal recognition difficulty, worst-case distinctiveness (wed). By integrating this oracle into gradient-based optimization process, avoid expensive exact evaluations and unlock a scalable, flexible design procedure. This enables three core advantages: (1) improved scalability, (2) support for general, potentially suboptimal agent models, and (3) extensibility to diverse constraints and objectives.
Our empirical evaluation highlights the effectiveness and versatility of the approach. In both classical grid worlds and complex Overcooked-Al environments, our method consistently outperforms baseline techniques in reducing wed while significantly lowering computational cost. Crucially, it remains effective under subop- timal agent behavior demonstrating robustness where many existing methods break down. Hunan-subject experiments further validate the practical utility of our framework, showing that it generalizes beyond sim- ulation and maintains its advantage even when agent models are learned from real human data. To our knowledge, this is the first work to evaluate GRD methods in a human-subject setting. Through abla- tion studies, we demonstrate that the predictive oracle plays a critica role in guiding effective environment optimization, with more accurate or expressive models leading to significantly better outcomes.
We assume uniform prior distribution over goals. As the agent takes action, we update the pasterior belief over goals through Bayesian updates based on the likelibood probability of the data-driven behavior model prediction.
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Limitations and future work. While our framework advances goal recognition design, several limitations remain. First, our approach requires large amount of data to train accurate predictive oracles. Although simulations can be used to generate training data, data from novel and richer environments is often scarce and presents challenges for simulation. Future work could explore several methods to address this limitation, including leveraging transfer learning (Pan & Yang, 2009) by pretraining on simulated environments and fine-tuning on limited data from new environments, as well as using generative models to produce synthetic yet behaviorally plausible training data (Goodfellow et al., 2014; Xu et al., 2019). Active learning techniques that reduce the amount of data required during collection also offer a promising direction. While these strategies require further validation, we believe they represent potentially viable and interesting avenues for applying GRD in data-scarce settings.
Second, we assume fully observable environments and stationary human behavior in this work. To address these limitations, future work could train the predictive model on inputs derived from belief state represen- tations, incorporating uncortainty in agent observations (Kaelbling et al., 1998) into the training process. In addition, the predictive model could be periodically fine-tuned using newly accumulated behavioral data, allowing it to adapt to changes in human decision decision-making over time.
Morcover, our investigation focuses on single-agent, discrete environments. To extend our framework to multi-agent settings, future work would need to model agent behavior in the presence of other agents, accounting for their interactions. To support continuous environments, the Lagrangian relaxation can be adapted to penalize changes using continuous distance functions such as norms, enabling gradient- bassdd optimization without altering the underlying pipeline. Overall, the modularity of our framework enables future work to address these limitations in targeted and flexible manner.
Broader impact. Finally, while our work aims to advance human-AT collaboration through goal recognition design, it is important to acknowledge the societal risks that may arise from its misuse.
First, designing enviromments that make human goals and intentions easier to infer could be misused. Sys- tems capable of anticipating intentions might be deployed not to assist users but to manipulate or steer their behavior. Because system designers typically hold an advantagcous position over decision makers within these enviromments, such capabilities can further amplify their influence over individuals. Second, since GRD relies predictive models trained on human behavioral data, it raises privacy concerns. Even when raw data are not directly exposed, adversarics could analyze model outputs or behaviors to infer sensitive personal attributes, creating opportunilies for profiling or surveillance. Third, by making goal inference more accurate and efficient, GRD could foster excessive reliance on AT predictions. Such overreliance risks under- mining human autonomy and weakening critical judgment, especially if users begin to accept AI inferences uncritically. Taken together, these risks highlight how technique intended to enhance collaboration could, under certain deployments, compromise user welfare and agency.
In light of these concerns, we discuss possible avenues for risk mitigation. On the technical side, privacy- preserving methods such as differential privacy could be integrated into the training of behavioral models, limiting the extent to which sensitive information is encoded and thereby reducing opportunities for exploita- tion. Moreover, incorporating uncortainty- aware methods into GRD could ensure that systems explicitly communicate the confidence of their inferences. Such mechanisms would help mitigate both privacy risks and overreliance by reminding users of the fallibility of Al systems. On the policy side, once the capabilities and risks of GRD are more fully understood, it will be important to weigh the potential benefits against the possible harms. This evaluation should guide the development of regulatory frameworks and ethical guidelines- for example, requiring that GRD-driven modifications not significantly reduce user autonomy relative to standard environments, and mandating transparency about the objectives and data underlying deployment. Establishing such safeguards will be essential to ensure that GRD is developed and applied responsibly, and that its benefits are realized without compromising broader societal values.
Acknowledgments
This work is supported in part by a J.P. Morgan Faculty Research Award and a Global Incubator Seed Grant from the McDonnell International Scholars Academy.
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A Experiment Details and Additional Results
In this section, we provide details of the experiments not included in the main paper due to space constraints. We also include and discuss additional experimental results.
A.1 Implementation Details
This subsection describes the implementation of the predictive model. We trained the predictive models on a simulated dataset generated by solving wed for randomly sampled environments with a specific agent behavior model. Several architectures were tested, including CNNs, Linear Models, Kernel Ridge Regression, and Transformers, with CNNs performing the best in predicting wed. The models processes inputs of the shape & x N N inputs, where k is the number of potential objects in N x N grid.
The CNN architecture used across the paper employs ResNet18 backbone with an adapted k-channel input layer, followed by three fully connected layers. Outputs are reduced to 32 and dimensions with Leaky ReLU activations and dropout, culminating in a single non-negative scalar via ReLU activation.
1.0
Training Loss Validation Loss
0.8
Wcd MSE Loss
0.6
For the experiments in Section 5, we trained CNN-based model on 100K data points, split into 80% training and 20% validation. The model achieved an MSE below 0.18 for both sets, with the validation set used for hyperparameter tuning. Figure 7 shows the training loss for the wed predictive model for the grid world domain (13 13) assuming optimal behav- ior. We used Adam optimizer and MSE loss and tested learning rates of 0.1, 0.01, 0.001, and 0.0001. A lcarning rate of 0.001 consistently produced the lowest validation error, enabling re- liable wed reduction across different setups.
0.4
0.2
0.0
2000 Number of iterations
1000
Figure 7: Training loss and validation errors for the CNN predictive model for wed with 13 x 13 grid world and optimal human behavior.
A.2 More Results for Run Time Comparisons
Due to space constraints and also that the results align with would expect, we do not include the time details for different approaches in the main text. We include the results here for completeness. Overall, as shown in Figure& 8, approaches that leverage the predictive model for wod are orders of magnitude faster than methods that require to evaluate wed during run-time. Note that the y-axis of the figure in log scale so the difference is in at least two orders of magnitude.
6
Exhaustive
2.5
Meain Log Time-ts (s1
Greedy (predicted wcd)
2.0
2-
Pruned-Reduce
Our approach
(true wed)
Mean Log Time
Greedy (true wed)
Greedy (predicted wcd)
Mean Log lime
1.0-
1.5
Our approach
Greedy (predicted wed)
0-
appreach
0.5
Greedy (true wed)
Gready (pradicted wcd)
0.0
Greedy (true wed)
1
Our approach
5
10
155
20
10
20 budget
30
40
10 budget
15
20
5
10 budget
15
20
budget
(8) Standard Setup (small)
(b) Standard Setup (large)
(c) Suboptimal
(d) Overcooked-Al
Figure 8: Run time taken by each method in the different experimental conditions. In the standard setup with small grid size, all methods except exhanstive complete within less than half second but our approach scales better with complex configurations.
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B Additional Experiment Results
In this section, we report the additional experiment results that not included in the main text due to space constraints. In Section 5.1 of the main paper, provided details of our performance with large grid size. In a smaller grid world, our approach achieves comparable performance to the baselines but it significantly outperforms them in larger grid sizes as shown in Figure 9.
Wcd reduction
wcd reduction w
3-
2-
Exhaustive
Exhaustive
Greedy (predicted wed)
Greedy (predicted wcd)
1-
Greedy (true wcd)
Greedy (true wcd)
Our approach
approach
10 budget
15
20
10 budget
15
(a) Individual budget
(b) Shared budget
Figure wed reduction in smaller (6 gridworld with optimal agent behavior.
B.1 Definition of Budget
In our evaluation, we compare the wed reduction relative to the budget allocated for modifications. In the grid-world domain, the budget represents the number changes made, which are limited to two types: blocking or unblocking cells. contrast, the Overcooked-Al domain allows for a richer set of modifications due to its complexity. Here, modifications involve changing the positions of objects. A valid environment must include all specified objects, detailed in Section 4.1.2. The budget in this domain is quantified the total Manhattan distance moved by the objects between the original and modified environments.
B.2 Langrange Parameter Space
In the main paper, we described how we relax the original constrained optimization problem by introducing a Lagrangian penalty parameter X, which indirectly controls the budget through pe- nalizing constraint violations. Since the budget cannot be specified directly, we instead vary X across a predefined range to explore different trade-offs between optimizing the objective and sat- isfying the budget constraint. Specifically, we sweep over log-scaled set. of values:, {0, 0.001, 0.002, 0.005, 0.007, 0.01, 0.02, 0.05, 0.07, 0.2, 0.5, 2, This range covers several or- ders of magnitude, allowing the optimization to balance constraint enforcement from very loose (small A) to very strict (large X) penalties. For all experiments, including those with single budget constraint, we used this same set of X values. In scenarios involving two constraints, such as Blocking and Unblocking constraints, we applied this range independently to each constraint, effectively exploring the joint penalty space by combining these values for each constraint.
e
B.3 Ablation Analysis
In the main paper, we provided the ablation analysis for the optimal behavior model with grid size of 13. Table 4 provides the same analysis for grid size 6. The results show mixed performance in this smaller environment, and our approach sometimes underperforms basclines. This reflects that our method's advantages emerge primarily in larger, more complex environments where traditional approaches become computationally intractable.
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Published in Transactions on Machine Learning Research (09/2025)
Table 4: Ablation results for grid world (size=6x6) showing the impact of different predictive models and optimization methods wed reduction across three environment modification settings, ie, Standard Setting, Individual Budget, and Shared Budget as described subsection 5.1. Each row represents a predictive model (e.g.. CNN) trained with a specified dataset size, learning rate, and associated training/validation loss. Due to poor performance, only the best Linear and Transformer configurations are shown. For each model, we compare two optimization methods: Greedy using predicted wed and proposed Approach, along with baseline using greedy optimization with true wod.
Predictive Model
Loss (mse)
Optimization Approach
wed Reduction
Train Validation
Standard Individual Shared
Baseline 1 (NA)
NA
NA
Exhaustive Search (True wed)
2.4=0.1
4.5+0.2
4.3+0.1
Baseline 2 (NA)
NA
NA
Greedy (True wod)
2.3=0.1
4.2:1..2
4.310.1
Greedy (Predicted wed)
1.1-0.1
16600.1
0.010.0
Linear (100K; 0.1)
1.9
Our Approach
0.4=0.0
1.4+0.1
1.4+0.2
Greedy (Predicted wed) Our Approach
0.0
0.410.1
0.0.0.11
Transformer (100K, 0.1)
3.0
3.0
0.0=0.0
0.1:0.1
0.4+0.1
Greedy (Predicted wed)
1,0=0.1
1440.2
1.5#0.1
CNN (1K, 0.001)
0.1
1.7
Our Approach
1.0=0.1
2.9
2.8+0.2
Greedy (Predicted wed)
2.0=0.1
3.7
3.6#0.1
CNN (10K, 0.001)
0.0
Our Approach
1.9-0.1
4.1+0..2
4.0+0.11
Greedy (Predicted wed)
2.1=0.4
3.820.22
3.5
CNN (100K, 0.001)
0.0
0.0
Our Approach
2.2-0.1
4.3+0..2
4.3+0..1
C Details of Simulations
To generate our training and evaluation datasets, we randomly generated environments and kept valid envi- ronments, e.g., those in which the goals are reachable and the objects don't overlap. Below, we provide more details about environment generation for specified grid sizes for both overcooked and grid-world domains.
C.1 Grid world
In grid world, valid environment includes a starting position, blocked cells, and two goal positions. The starting position is randomly placed in the first column, and the goal positions are randomly placed in the last two columns, The number of blocked positions in each grid is randomly selected from range of 0 to 2x the grid width. We discard any assignments that make the goals unreachable. For experiments with suboptimal behavior, we also randomly assigned small subgoal rewards to unblocked cells that the agent would collect on its way to the goal state. The two goal states are assigned a large reward that is 10 times the largest subgoal reward.
C.2 Overcooked-Al
In Overcooked-Ar AI, a valid environment includes one pot, one tomato source, one onion source, one dish source, one serving point, no open spaces at the border, and any number of open spaces and blocked cells. All objects must be reachable from the agent's randomly assigned starting position, with the number and positions of blocked cells assigned randomly. The agent is randomly assigned one of two goals for each experiment, where both goals are randomil selected from the set of three possible recipes: three-lomato soup, three-onion soup, or mixed soup. Each goal has the same randomly assigned reward value. Suboptimal behavior is modeled by assigning small random subgoal rewards when adding ingredients to the pot.
Details of Huban-Subject Experiment
Lastly, we include more information about our human-subjoct experiments. In the human-subject experi- ment, each worker is asked to play navigation game in x 6 grid world environments. The task interface is shown in Figure 10.
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Published in Transactions on Machine Learning Research (09/2025)
Note that while each environment has two goals, only show goal (the goal of the worker) to the worker in our interface to simplify the presentations. The second goal is shown blocked cell in the interface, i.e the worker only navigates to the shown goal.
Gume Information
Gume: interface
Your marked and your the
gril..
W
Gumes: 1/15
Figure 10: The interface of our human subject experiment.
We have recruited 200 workers from Amazon Mechanical Turk in total, and Table 5 contains the demographic information of the workers.
Table 5: Demographic information of the participants in experiment.
Group
Category
Number
20 29
84
30 39
76
Age
40 to 49
26
50 or older
14
Female
89
Gender
Male
110
Other
Caucasian
175
Black or African-American
8
American Indian/Alaskan Alaskan Native
3
Race / Ethnicity
Asian Asian- Ammricnm
8
Opanish/Hispann
Other
5
High school degree
5
Some college credit, no degree
5
Associate's degree
4
Education
Bachelor's degree
135
Graduate's e degree
49
Other
2
E
Computation Details
All experiments were run on a computing cluster equipped with 40 CPU cores (Intel Xoon Gold 6148 @ 2. 2.40GHz), single NVIDIA Tesla V100 SXM2 GPU (32GB), and up to 80GB of memory. To ensure reproducibility, worked within clean and consistent software environment built around Python 3.10 and widely used scientific librarics. PyTTrch was our main deep Icarning framework, with NumPy and pandas handling numerical computation and data processing. During model training and the discrete gradient descent. optimization, we relied on PyTorch's autograd system to compute gradients automatically and efficiently.
20


Reviews:
[{"review_id": "V5j6HbkaGc", "reviewer": "Reviewer_r8iU", "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**\n1. **Clear Motivation and Problem Setup:** The paper addresses two critical limitations of existing GRD methods—computational inefficiency and reliance on optimal agents—and proposes a reasonable ML-based alternative.\n\n2. **Comprehensive Experiments:** The simulations span from simple grid worlds to complex Overcooked-AI environments, showcasing the adaptability and scalability of the proposed method.\n\n3. **Human-Subject Evaluation:** Including human behavior modeling and evaluation adds practical relevance and broadens the contribution.\n\n4. **Runtime Efficiency:** The approach is shown to significantly reduce runtime over traditional exhaustive or greedy methods.\n\n**Weaknesses**\n1. **Methodological Simplicity:** The core approach—training a CNN to approximate wcd and using it in gradient-based optimization—is straightforward. There is limited theoretical depth in either the learning or optimization component.\n\n2. **Lack of Theoretical Guarantees:** The paper lacks formal analysis on convergence, generalization bounds of the predictive model, or approximation quality of the learned wcd.\n\n3. **Limited Novelty in Learning/Optimization:** Both the learning (standard supervised regression) and the optimization (basic discrete gradient descent with Lagrangian relaxation) are adaptations of well-known techniques.\n\n4. **Heavy Dependence on Simulated Data:** The method requires a large volume of labeled simulation data for training, which might not generalize to settings where such data is unavailable or unreliable.\n\n5. **Sparse Discussion on Failure Cases:** The limitations of the learned wcd model or optimization getting stuck in local minima are acknowledged but not thoroughly studied.", "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 introduces a data-driven framework for goal recognition design (GRD) by learning a predictive model of worst-case distinctiveness (wcd) and using gradient-based optimization to efficiently modify environments, accommodating suboptimal agent behaviors.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "1. How sensitive is the optimization outcome to inaccuracies in the wcd predictor, especially in edge cases?\n\n2. Can the framework generalize to multi-agent settings, or does it fundamentally rely on single-agent assumptions?\n\n3. Are there theoretical guarantees or empirical evidence that the proposed gradient-based optimization avoids poor local minima better than greedy baselines?\n\n4. How would the method perform if applied to continuous action/state spaces, or domains without grid-like structure?\n\n5. What is the role of agent model misspecification (e.g., in human modeling) on the robustness of the learned environment design?", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "B9TKII4VMd", "reviewer": "Reviewer_fT8z", "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:\nStrong Aspects: (1) Addresses Key Limitations of Prior Work: The paper effectively tackles the computational demands and the unrealistic assumption of optimal agent behavior prevalent in existing Goal Recognition Design (GRD) methods. (2) Novel Data-Driven Optimization Framework: The core contribution of leveraging machine learning to predict \"worst-case distinctiveness\" (wcd) and integrating it into a gradient-based optimization framework is a significant advancement. This approach allows for efficient evaluation and optimization. (3) Improved Runtime Efficiency: The simulations clearly demonstrate superior runtime efficiency compared to traditional exhaustive search and greedy baselines, especially in larger and more complex environments. (4) Human-Subject Validation: The inclusion of human-subject experiments to validate the method's effectiveness with real human decision-makers is a significant contribution and a first for this research area.\n\nOther key strength would be that the paper presents extensive simulations and ablation studies across various settings and agent models, providing strong evidence for the proposed method's effectiveness.\n\nWeaknesses:\n\n(1) Reliance on Abundant Data for Predictive Model: The paper acknowledges that the approach depends on \"abundant data to train a reliable wcd predictor\". While simulations are used to generate data, the scalability of this data generation to \"richer domains\" is questioned. Authors could further discuss strategies for data-efficient training or transfer learning in scenarios where abundant real-world data is scarce. (2) Static and Fully Observable Settings Assumption: The current framework assumes \"static, fully observable settings\". This is a limitation for real-world applications where dynamic and partially observable environments are common. While mentioned as future work, a brief discussion on the challenges and potential initial steps towards addressing these complexities would be beneficial.", "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 submission introduces a novel data-driven optimization framework for Goal Recognition Design (GRD) that significantly advances the field by addressing key limitations of existing approaches. The core innovation lies in using machine learning to predict \"worst-case distinctiveness\" (wcd), a metric for how difficult it is to infer an agent's goal. This predictive model is then integrated into a gradient-based optimization framework, enabling efficient modification of decision-making environments to improve goal recognition. The new knowledge presented includes: (1) The machine learning oracle dramatically reduces the computational overhead associated with evaluating wcd, leading to significantly faster runtime compared to traditional exhaustive search methods. (2)  Unlike prior GRD methods that often assume optimal or near-optimal agents, this framework explicitly incorporates diverse agent behavior models, including suboptimal and data-driven human behavior models, making it more realistic and broadly applicable. (3) The approach extends to complex environments like Overcooked-AI and settings with flexible budget constraints, where existing methods are not applicable. (4) The study includes real-world human-subject experiments, demonstrating that the proposed method creates environments that genuinely facilitate efficient goal recognition from human decision-makers, a first for this area of research. This confirms the practical utility and real-world applicability of the framework beyond simulations.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "Critical Adjustments for acceptance: \nDiscuss Data Scarcity and Scalability to Richer Domains: The paper acknowledges the reliance on \"abundant data to train a reliable wcd predictor\" and raises concerns about scaling to \"richer domains\". It is critical to include a brief discussion on potential strategies for addressing data scarcity (e.g., data augmentation, transfer learning, or efficient data collection techniques for real-world scenarios) or how the framework might be adapted when abundant simulation data isn't feasible.\n\nAdjustments to Strengthen the Work:\n\n(1) Address Dynamic and Partially Observable Environments: The paper currently assumes \"static, fully observable settings\". While mentioned as future work, briefly outlining the conceptual challenges of extending the framework to dynamic and partially observable environments, or suggesting initial research directions, would demonstrate a forward-thinking perspective and strengthen the paper's vision. \n(2) Discuss Non-Stationary Agent Behavior: The paper notes that \"real human preferences often shift\". While acknowledged as a limitation and future work (adaptive or online behavior models), a brief discussion on how the framework could conceptually be adapted to non-stationary human behaviors, perhaps by incorporating adaptive learning components or mechanisms for preference elicitation, would enhance its realism.", "broader_impact_concerns": "The work presented in the paper, \"Goal Recognition Design for General Behavioral Agents using Machine Learning,\" primarily focuses on improving the efficiency and applicability of goal recognition design in human-AI collaboration. However, there are a few ethical implications that warrant consideration and could necessitate a broader impact statement: (1) Potential for Manipulation or Unfair Advantage, (2) Privacy Concerns from Behavioral Data, (3) Dependence and Over-reliance: As AI systems become more adept at understanding and influencing human behavior through GRD, there's a potential for humans to become overly reliant on these systems, potentially diminishing their critical thinking or decision-making skills over time.\n\nA broader impact statement would be crucial to acknowledge these potential negative implications and outline steps taken or planned to mitigate them, such as: focusing on transparency, ensuring user control, implementing robust data governance, promoting diverse and representative data collection, and rigorously testing for biases.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "TMuNpLw6fd", "reviewer": "Reviewer_dHQo", "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\nThe approach proposed in this paper is conceptually well-explained. The experiments are done throughly to support the authors' claims, especially the real world human dataset collected by the authors. \n\n## Weaknesses\nIn general, the technical details in this paper should be mentioned more explicitly, and some properties of the proposed approach should also be discussed. See requested changes for more detail. Besides, the authors also mentioned several reasonable limitations of this work in section 6.", "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 presents a data-driven framework for goal recognition design that improves scalability and accounts for general, including suboptimal, agent behavior. The authors train a predictive model to estimate the difficulty of goal recognition via worst-case distinctiveness, and use it in a gradient-based optimization process to modify environments efficiently. Their method outperforms existing approaches in both worst-case distinctiveness reduction and runtime, scales to complex settings, and handles flexible constraints. Human-subject experiments further demonstrate its effectiveness in enhancing goal recognition for real-world human decision-makers.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "The authors may revise their manuscript according to the following questions:\n* In the first paragraph of page 5 (optimization procedure), the authors proposed to solve the problem (1) via optimizing over the unconstrained Lagrangian relaxation. Since strong duality does not hold here and the dual problem is not solved, the obtained optimal point $w'$ is not globally optimal. While I do not think this should be an issue in practical applications, the authors mentioned on top of page 8 that \"...as our optimization procedure accounts for the available budget and avoids getting trapped in locally optimal solutions\". So I am wondering why this claim hold? Was this conclusion made from explaining the experiment data, or did I missed something?\n* Based on the previous question, the budged constraints in the prolem (1) can (and are likely to be) violated if one simply optimizing the Lagrangian without carefully tuning the $\\lambda$. So I am wondering is the budged really a hard constraint such that any violation would be unacceptable, or it can be violated to some extend that should be judged ad hoc by the user? If it is the first case, how to select an appropriate $\\lambda$ value would then be crucial, so it would be helpful to mention in the experiments how the authors selected the $\\lambda$ such that the constraints were guaranteed not to be violated. If it is the second case, mentioning how much the constraints were violated in individual experiments for a reference.\n* Technically, how did the author calculate gradient with respect to the Lagrangian? I suppose this information can be found in the code provided by the author in the supplementary, but I do believe explicitly mentioning this out would be helpful for the potential users of the proposed algorithm.\n* As a follow up to the previous question, the authors mentioned that in general the modifications to the environment would be discrete, is this because of the discrete nature of the environment? If it is the case, although the following question would then be out of the scope of this paper, I am wondering how could one obtain the gradient over $w'$ if the environment is continuous?\n\nMinor:\n* In the \"comparing the accuracy of goal inference\" paragraph of page 12, it would be helpful to describe in more detail about how the off-the-shelf Bayesian inference algorithm works, or at least adding a reference, so that the readers would have a better idea about what was done here.", "broader_impact_concerns": "No.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)