An Offline Adaptation Framework for Constrained Multi-Objective Reinforcement Learning
Authors: Qian Lin
Zongkai Liu
Danying Mo
Chao Yu
Venue: NeurIPS 2024 poster (2024)
Keywords: Multi-Objective RL
safe RL
offline RL
Primary area: reinforcement_learning

Abstract: In recent years, significant progress has been made in multi-objective reinforcement learning (RL) research, which aims to balance multiple objectives by incorporating preferences for each objective. In most existing studies, specific preferences must be provided during deployment to indicate the desired policies explicitly. However, designing these preferences depends heavily on human prior knowledge, which is typically obtained through extensive observation of high-performing demonstrations with expected behaviors. In this work, we propose a simple yet effective offline adaptation framework for multi-objective RL problems without assuming handcrafted target preferences, but only given several demonstrations to implicitly indicate the preferences of expected policies. Additionally, we demonstrate that our framework can naturally be extended to meet constraints on safety-critical objectives by utilizing safe demonstrations, even when the safety thresholds are unknown. Empirical results on offline multi-objective and safe tasks demonstrate the capability of our framework to infer policies that align with real preferences while meeting the constraints implied by the provided demonstrations.

An Offline A Adaptation Framework for Constrained Multi-Objective Reinforcement Learning
Qian Lin', Zongkai Liu', Danying Mo', Chao Yu 12.3f
Sun Yat-sen University, Guangzhou, China
PPengcheng Laboratory, Shenzhen, China
3 'MoE Key Laboratory of Information Technology, Guangzhou, China [1inq67, liuzk, mody @mai 12. sysu. edu. cn, yuchao3@mail sysu. edu.
Abstract
In recent years, significant progress has been made in multi-objective reinforcement learning (RI.) research, which aims to balance multiple objectives by incorporating preferences for each objective. most existing studies, specific preferences must be provided during deployment to indicate the desired policies explicitly. However, designing these preferences depends heavily human prior knowledge, which is typically obtained through extensive observation of high-performing demonstra- tions with expected behaviors. In this work, we propose a simple yet effective offline adaptation framework for multi-objective RL problems without assuming handcrafted target preferences, but only given several demonstrations implicitly indicate the preferences of expected policies. Additionally, we demonstrate that our framework can naturally extended meet constraints on safety-critica objectives by utilizing safe demonstrations, even when the safety thresholds are unknown. Empirical results on offline multi-objective and safe tasks demonstrate the capability of our framework to infer policies that align with real preferences while meeting the constraints implied by the provided demonstrations.
Introduction
In the standard reinforcement learning (RL) setting, the primary goal is obtain policy that maximizes cumulative scalar reward (Sutton and Barto 2018). However, in many real-world applications involving multiple objectives, a desired policy must only strike a balance among potentially conflicting objectives but also consider the constraints imposed on specific safety-critical objectives. Such requirements motivate the research of Multi-objective RL (MORL) [Liu et al.) 20044] Mossalam et al., 2016) and safe RL [Gu et al., 2022 Achiam et al. 2017]. In addition to reward maximization, former aims to enable policies that cater to a target preference indicating the trade-off between competing objectives, while the latter focuses on reducing the cost measures of learned policies within given safety threshold.
Despite the development of meticulous and effective mechanisms to achieve these goals, most existing MORL and safe RL algorithms rely predefined target preferences or safety thresholds. These ele- ments need to be carefully designed by human experts with prior knowledge, generalized from a large number demonstrations through observation. Taking autonomous driving an example, defining aggressive, stable, and conservative strategies through different preferences between minimizing energy consumption and increasing driving speed may require extensive human participation, which means that researchers need to categorize driving data into different styles based on human experience and observe the energy consumption-spe speed ratio to estimate appropriate preference weights and
CCoresponding author
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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safety thresholds for different strategies. Moreover, it is uncertain whether policies based on manually designed preferences will exhibit expected behaviors or whether feasible policies exist under given safety constraints. The challenge of designing appropriate preferences or safety thresholds becomes more pronounced as the number of objectíves increases.
Compared to manually designing target preferences or safety thresholds based on human knowledge, it is more natural infer expected behaviors through a few demonstrations that implicitly indicate the trade-off between multiple objectives and the constraints of safety. For instance, selecting demonstrations with conservative behaviors from the driving dataset can be easier than inferring preferences that lead to conservative policies. Therefore, in this work, we formulate novel offline adaptation problem for constrained MORL. with the goal to leverage a few demonstrations with expected behaviors, rather than relying on handcrafted target preferences and safety thresholds, to generate a target policy that achieves desired trade-offs across various objectives and meets the constraints on safety-criticll objectives under offline settings.
To achieve this, we first focus on unconstrained MORL scenarios and propose a simple yet effective offline adaptation framework Preference Distribution Offline Adaptation (PDOA), which includes: 1) learning a set of policies that respond various preferences during training, and 2) adapting a distribution of target preferences based on a few given demonstrations during deployment. Specifi- cally, we initialize the first part with existing of-te-ofthhearr offline MORL algorithms, and then in the second part, we propose to align the adapted policies with expected behaviors by modeling the posterior preference distribution regarding demonstrations. Moreover, we show that our framework can be extended to constrained MORI, settings by converting a constrained RI. problem into an unconstrained MORL counterpart, and incorporating a conservative estimate of preference weights on constrained objectives to mitigate the potential constraint violations. Lastly, we conduct several empirical experiments on classical MORL, safe RL tasks and novel constrained MORL environment under offline settings, demonstrating the capability of our framework in generating policies that align with the real preferences and meet the constraints implied in demonstrations.
2 Related Work
Multi-objective RL Many existing MORL methods explicitly maintain a set of policies tailored to various given preferences to approximate the Pareto front of optimal policies. These works either apply a single-pllicy algorithm individually for each candidate preference [Roijers et al. 2014 MMssalam et al. 2016), employ evolutionary algorithms to generate a population of diverse policies Handaa| 2009 Xu et al. [2020] or simultaneously learn set of policies represented by single network [Aells et al. 2019 Basaklar et al. 2022]. Furthermore, due to the potential costs and risks associated with extensive online exploration, several studies (Zhu et al., [023 Lin et al.) 2024] have been proposed to leverage only offline datasets for MORL. by extending offline reurr-condiitoned
methods Chen et al. 2021 Emmons et al., 2021] offline policy-regularee
methods (Fujimoto and
Gu 2021 Wang et al. 2022 to MORL settings. Despite the ability to obtain a set of well-performing policies for various preterences, most existing MORL methods overlook the process of acquiring target preferences for identifying appropriate policies during practical deployment. In this work, we assume online interactions and no target preferences but several demonstrations generated with expected behaviors, which are easier to access than meticulously designed target preferences.
Safe RL While maximizing the expected reward, classical safe RL methods restrict the cumulative cost to stay within a predefined safety threshold through Lagrangian primal-dual methods (Stooke) et al. 2020 Chow et al. 2017) or primal approaches [Xu et al. 2021 SSotla et al., [022). Recently, several studies have focused on learning a set of policies that respond to various safety thresholds in both online settings (Yao et al. 2024a and offline settings (Liu et al.) 2023a| Lin et al. 2023).
Similar to MORL, these works also assume access to well-designed safety thresholds that ensure safe behaviors. Unlike prior research, our framework relies solely on safe demonstrations to indicate the implicit constraints and offers a mechanism to mitigate constraint violations through conservatism.
RL with Offline Adaptation Several studies have applied meta- meta-learning techniques to address MORL [Chen et al.) 2019) or safe RL problems [Guan et al. 2024a), but they require online interactions for task adaptation and suffer from low sample efficiency. Additionally, other research endeavors explore offline adaptation methods to mitigate environmental uncertainty by modelling a posterior distribution over all possible Markov Decision Processes (MDPs) Ghosh al. 2022 or

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considering varying confidence levels in conservative value estimates [Hong et al. [022] [Mitchel| al. 2021 Xu et al. 2022a] focus on offline adaptation for multi-task problems, aiming achieve fast adaptation to new downstream tasks after offline training on multi-task experience. Among these methods, offline meta RI. [Mitchell et al. 2021] addresses a problem similar to ours, which aims to train meta policy that can adapt to new task with limited data. Prompt-D'T (Xu et al. 2022a] achieves quick adaptation to new tasks by incorporating a few demonstrations as prompts into the decision transformer [Chen et al. 2021] framework. We present further discussions about the difference between multi-task RL and our setting in Appendix A.T
3 Preliminaries
3.1 Constrained Multi-Objective MDP (CMO-MDP)
Both multiple-objective RL and safe RL can be discussed based on a uniform formulation: constrained multi-objective MDP (CMO-MDP) proposed by LP3 [Huang et al. [022]. A CMO-MDP is defined as a tuple (S, A, P, r, c, B, 7) with state space S, action space A, transition distribution ((8'|s, a), vector reward functions E R for N unconstrained objectives, vector cost functions E R safety thresholds 3 E R for K constrained objectives and discount factor E [0, 1]. The goal to maximize the rewards on unconstrained objectives while ensuring the costs on constrained objectives remain within the safety threshold B. Since it is typically infeasible to maximize all task objectives simultancously, preferences w E 92 and preference functions (r) which map the reward scalar utility under specific preference w. are introduced to control the trade-off between unconstrained objectives. Given preferences w E Ω and safety thresholds (3, the goal can be formulated as follows:
max Tw.p
Rww
s.t.
C33
(I)
where R. Ee (rr) and C E, Cs represent cumulative utility and vector cost over time t, respectively. We denote Tw.3 as a policy conditioned on w, B.. this paper, we consider the linear preference setting (i.e.. (r) = w where w E RN and ||w|| = 1), which is widely studied and applied (Mossalam al. 2016 Abels et al.
2019] and also serves a bridge between unconstrained
and constrained MORI,, as shown in Section 4.3 A CMO-MDP problem can degenerate to a standard
safe RL problem when N- and to standard multi-objective problem when K = O.
3.2 Offline MORL
Under offline MORL settings, offline dataset D s', is the only data available for training, which is generated by a set of behavior policies TT(-|w) with diverse behavioral preferences w. One straightforward yet effective approach to learn a set of policies for various preferences is to adapt offline single-objective RL methods for MORL settings. An example of this approach is the multi-objective version of Diffusion-QL (MODF) [Lin et al. 2024], which incorporates a preference-condicee conditiond policy (i.e., T(ass, w)) and a dimeniddimesionnll value function for N objectives (i.e., Q(+ a, w) (1, QN (s, a, w)) into Diffusion-QL. [Wang et al. 2022
L -E(,,,,) [ (Ea [w QQQ (s, ww)
<IE KIB4,el |||e ealaaaaaa + vI The 1111]
LQ CQ==E Be,.a,,, wD [(r ( Q w) Q(s,
where i the diffusion timestep, k is the regularization weight, a; are pre-defined parameters of diffusion model and ca(-) is denoiser model. The diffusion policy generates the actions by iteratively using e-(-) I) to recover actions from noise. The second term in the actor loss of Eq. 22) a diffusion reconstruction loss, which serves regularization term to align the actions of diffusion policy with the behavioral actions in the dataset.
Pareto-Effiicies Decision Agents (PEDA) Zhu et al. 2023 is another MORL method based on supervised RL, which trains a policy conditioned on both target preferences and vector returns through a supervised paradigm:
L = - [log [og.
(3)
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where T:r = {(s,, Tz), .... @r.ar..ri is trajectory segment, = 1/= Te is the target vector return (a.k.a,, return-to-go) and is the behavioral preference of T::T- It is worth noting that despite the significant performance of the above two methods in offline MORL problems, both require human-prove -uman-provided target preferences during deployment to achieve the desired behavior, and therefore cannot be directly applied to the setting in this paper.
An Offline Adaptation Framework for Constrained Multi-Objective RL
4.1 Problem Formulation of Offline Adaptation for CMO-MDP
In this paper, focus novel offline adaptation problem for constrained MORL, with the goal to leverage only a few demonstrations to generate the policies that exhibit expected behaviors. During training, an offline dataset D {(s,a, 8', rr w)} is provided for policy training. During deployment, we have access to a demonstration set corresponding to a target i.e.
Bg
where x; is defined as a tuple (s,, Os s Ts ci) and M is the total number of transition demonstrations. The target G can be preferences in MORL problems (G wy), safety thresholds in safe problems (G = 3yy) or combination of both (G (Wg. Bg)), and मड is the expert policy that achieves the best utility and meet the constraints under the preference wl and safety threshold Bg of the target G. our setting, the real target G is inaccessible, and the goal is to obtain an adapted policy for the target G' that ensures high utility (r) and meets the constraints with safety threshold B by leveraging demonstration set Bg during the deployment phase.
4.2 Offline Adaptation for the Unconstrained Case
First, we set aside the constraints in CMO-MDP and focus on the unconstrained version. Our proposed framework, Preference Distribution Offline Adaptation (PDOA), solves the offline adaptation problem under unconstrained settings in two steps: 1) learning set of policies that respond to various preferences during training; and then 2) adapting a distribution target preferences based on given demonstrations during deployment.
In the first part, directly apply existing offline MORL algorithms on the dataset D to obtain a set of policies f. that respond to varying preferences w. In the second phase, we propose to model the distribution of target preferences and then utilize this distribution obtain reliable estimation of target preference. Specifically, we consider the posterior probability of the target
preference W/ with regard to demonstration set B i.e., (u,, D) P(Bw, P(w,, D)
P(B.,, ())
Here P(B,, (wg. D) represents the probability that the optimal نū, generates samples Bw, in the real environment ((s', rls,, a). Due to the inaccessibility of P and स under offline settings, we replace them with the empirical dynamics (s'ls, a) and its corresponding optimal policy # which can be obtained using offline data D during training. Therefore, the preference posterior distribution be approximated by
Plw|Bwo D) P(Bw, w, D) P(Bw, (Ms Rt. (Ww
=
P(Bwg (D)
P(Bw,
M
x P(w|D) II Pap (s))t (s rslss,
where (si, (si,0;, ri, s() E Bwyy One challenge in Eq. is the requirement of explicitly modeling the state distribution P=ş (s;) and the transition probability (w rils;, Another concern is that demonstrations Bi, with the target preference Wa can be out-of-distribution samples for the estimation of A and Mu, leading to considerable discrepancy between estimated P#: (s:). Pu,(s/ relst, a;) and their real-world counterparts. This challenge is pronounced in multi-objective settings due to significant differences in the trajectory distributions of the optimal policy under various preferences. Therefore, following previous offline adaptation works Ghosh et al. 2022
Hong et al.)

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2022], we opt to approximate log P= (s)))s (s ralst, a;) with surrogate defined by TD error of value models of f Mw:
(6) where 5 is a hyperparameter. This approximation makes sense because (8, a, r,)") not only measures how likely the sample (s, a, r') occurred during training for preference w but also aligns with the estimated dynamics Pw. In other words, - a, r, s') has a high value if (s, a, r, s') is an in-distribution sample relative to the training datasets under preference and occurs with a high probability in Mw-
(,,,,,,)) - ( w)))
Then, we fit the posterior P(w D) with Gaussian distribution Mu, ol) with parameters a E Rº and R by minimizing their Kullback-Leibler divergence, leading the following adaptation loss:
Lu 0) =DK =DxL(Po(W)]|P(u Buy D))/M + mill - 1)2
M
1
=- BuNN((HO))
TD (8,, Gg Ps, 8/) + log a (1)1s),
M
log P(w D)
H (po)
M + (llleell2 1)2
M
where the term 7 (1111111111101111 with hyperparameter regularizes ||عl|| to be close to 1. We approximate the prior distribution (DW)D) with a Gaussian distribution fit to the behavioral preferences training data D. Eq. (7) indicates that w is likely to be the target preference wy if it corresponds to high T (s;, us: Taa 8,), log # (a, (e, w) and P(w] (D), which means: 1) the demonstration set Bw, appears with high probability in both the training set and M 2) # (arls; (s. w) is likely to generate the actions in : and 3) w stays within the prior preference distribution with high probability. We justify the effectiveness of this approach with the empirical results in Appendix A.9 where -. (5s, aty Pú, s() (called TD reward) and 4% (ae ( w) (called action likelihood reward) shows a strong correlation with the real target preference.
Implementation The first part of our framework PDOA is instantiated with state-of-the-ar MORL algorithms: MODF and the best algorithm MORvS in PEDA mentioned in Section 3.2 to learn set of policies that responds to various preferences. We refer to these two instances as PDOA [MODF] and PDOA IMORvS]. The well-trained policies and their corresponding value functions obtained by MORL algorithms during training are utilized to calculate the action likelihood reward #2 and TD reward r (-) in Eq. (7). During deployment, the preference distribution pe (w) is updated through the adaptation loss 7 on the demonstration set Bw,, Finally, we obtain an adapted target preference w, = |//|| and policy A (-(w>,) that aligns with the real target preference w, implied
in demonstrations Bwg. More details about implementation can be found in Appendix A.5
4.3 Extension to Constrained Settings
Then, we consider a natural extension of our MORL adaptation framework to constrained settings. Under the linear preference setting, the constrained MORL problem in Eq. (T) can be converted to its dual form with zero duality gap [Paternain et al. 2019:
min maxE XER
JwJn AT
Σ c c (3)
(8)
Denoting X" as the solution of this problem, the dual problem g can be rewritten as:
max Ex II 1 1 [r], -c11'
(9)
This formulation means that the constrained MORL problem under safety threshold ,3 is uniquely equivalent to an unconstrained problem of finding the optimal policy under an extended preference و = w [+T]T/I[ww) A * among extended + K objectives = -r]-- However, solving for the extended preference is challenging and requires the real safety thresholds, which
5

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are inaccessible in our setting, Nevertheless, Section 4.2 preferences from the demonstration set, helping us circumvent this challenge. Therefore, we can convert a constrained MORI problem to unconstrained MORL problem, where the vector reward is defined f [r,, -ca] and dataset D is augmented to D. Here, F1.N corresponds to N unconstrained objectives, while +NNN = -c associated with constrained objectives. One issue with this approach is how to set the behavior preference for augmented dataset D. We present an effective scheme for approximating behavioral preferences in Appendix A.5
provides an approach to infer the target
However, one concern about this approach is the estimation error between the adapted preference R obtained through Eq. 7 and the real preference Wg associated with the problem | due to the insufficiency of demonstrations. This discrepancy can lead to constraint violations when the preference weight of the adapted preference Wa constrained objective is less than the one of / (i.e.. Wa): < [Wy] for any i E {N + 1. ...,, N + })) Therefore, we propose to apply a conservative constrained objectives by neglecting the minimum value with probability 1- - a in the adaptation distribution w ~ N(,, o). Specifically, the preference weights on the th objective is estimated as follows:
estimate of preference weights
VaR. (Io))) = μe + a, b, = CVaRa ((3),) ["'
p ((0 . N N (10)
1-a
a
and b, = μi for 1 S - N. Here, VaR is the value of risk and CVaR is the conditional one, and ((x) = v2w exp(- 12. is the standard normal p.d.f., and ((x) is the standard normal c.d.f., The parameter in Eq. (IO) controls the conservatism of the estimation of preference weights. For all constrained objectives, a < results in a conservative estimate b, > μ4; reducing the risk of constraint violation. Additionally, as the number of demonstrations increases, the standard deviation o, decreases, and thus b, will move towards μú resulting in less conservatism. In the end, we obtain the adapted target preference W. b/||b|| and the adapted policy πt (ssaa, Wa).
5 Experiment
In this section, we conduct several experiments on classical MORL environments in Section 5.] and safe RL tasks in Section 5.2 to evaluate our framework in achieving preference alignment and approaching constraint satisfaction. respectively. Then, we test our method set of new constrained MORL (denoted as CMORL) tasks in Section Finally, we discuss the effectiveness of the components of our method in Section 5.4
Environments and Datasets In Section we utilize the D4MORL datasets ZZhu et al. 2023 for MORL experiments, which involve two conflict objectives and variety of behaviors based on preferences in multi-objective MuJoCo tasks. In Section 5.2 all algorithms are trained on the datasets from DSRL benchmark [Liu al. 2023b which involve ve constrained objective and an unconstrained objective in BulletSafeGym tasks Gronauer 2022 In Section 5.3 we develop set of CMORL tasks by incorporating an additional velocity constraint the original mujti-objecttve MuJoCo environments and collect datasets from these tasks. Thus, these environments contain two unconstrained objectives and one constrained objective. More details about these environments and datasets can be found in Appendix A.2 We construct training sets and demonstration sets based on the above datasets and present the details on Appendix AA.3
Evaluation Protocols
For evaluation, we define target set T = (G), with each target G corre- sponding to a demonstration set B& that meets the target G. For MORL tasks in Section [.1] G is a target preference wg. All target preferences are selected from the dataset's preference support set at fixed interval 0.01 (i.c., wa = [0.01k, 1 0.01k], s.t. min i < Wg I max i where k = 0, 100 and @ is the behavioral preference of the dataset). For safe RL tasks in Section 5.2 G is a safety
threshold By. All safety thresholds are set to 6 equidistant points within the range of possible thresholds. The target of CMORL tasks in Section 5.3 5.3 is (wi., Gy), the Cartesian product of the target preference spaced at 0.1 interval and 6 equidistant safety thresholds.
We utilize BG to generate adapted policy for each target G and gather 5 trajectories from environ- ments to assess its expected vector return. For tasks without constraints, we present the average utility and Hypervolume metries to demonstrate the overall performance across all targets and the diversity

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of adapted policies. For tasks with constraints, we group the adapted policies by safety thresholds and report the maximum cost return on constrained objectives and average utility and Hypervolume on unconstrained objectives for each group. We perform 3 runs with various seeds and report average performance along with 1-sigma error bar. More details about metrics can found in Appendix [A.4
Comparative Algorithms category is preference/tresholde -agnoosi baselines that have no access to the real target preferences or safety thresholds implied in the demonstrations, including: 1) BC-Finetune, where the policy learned on training dataset via behavior cloning and fine-tuned on demonstration sets and 2) Prompt-MODT, multi-objective version of Prompt-DTT [Xu et al. 2022a] that transforms multi-objective scenario into multi-task problem via preference-based division and achieves offline adaptation for various tasks by taking demonstrations category is preference/tbreshold fifecrenc/ttreshood--ffnnne iinfoomeed baselines that have access to the implied preferences and thresholds and thus serve the oracle benchmark, including: 1) original MODF and MORvS for MORL tasks, 2) CDT [Liu et al., 2023a] for safe RL tasks, which makes decisions based on given safety thresholds to ensure constraint satisfaction for various thresholds. For CMORL tasks, instead of adapting the preference through demonstrations, we enumerate all possible augmented preferences of MODF with a small interval and report the best performance under these preferences the oracle. More details about comparative algorithms are placed in Appendix A.4
The algorithms for comparison are divided into two categories. The first
prompts of the transformer. The second
5.1
Preference Alignment for MORL Tasks
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MD-Hallhheetabb2 1st
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MC-Nillrr260 Ist
2.30
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P004 (aconvs)
Prampt etror
BC Foettnee
PDRTA (MODF))
Promept MOOo
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PDDA (8000))
pode (scons))
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PODA (N6209))
Po04 (MCRYs)
Frongt Prrpt-MoTT
BC: Fietune
Aug Utility
Hypervolume
Avg Utility Oracie
Hypervolume Oracle
Figure Results on D4MORL Amateur datasets. Higher average utility and Hypervolume are
preferable. The dashed lines represent the best performance between the original MODF and MORvS.
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PDDA| (olls)
ProppSOOT
BC PC
Figure 2: Pareto fronts different algorithms on D4MORL Amateur datasets. Each point represents an adapted policy for specific unknown target preference.
The average utility and Hypervolume of all algorithms are shown in Figure Our method demon- strates superior overall performance and matches the oracle performance of preferencc--nfoomeed methods. Moreover, we present the Pareto fronts of different algorithms in Figure 2 Our method produces broader and expanding Pareto front compared to BC-Finetune and Prompt-MODT, which indicates that the adapted policies of our method exhibit higher diversity and better performance. Meanwhile, we observe that the adapted policies obtained by BC-Finetune cluster around the behavior- cloned policy, and thus BC-Finetune obtains the narrow Patero fronts and low Hypervolume, which indicates the difficulty of changing the policy's preference through simple fine-tune with limited samples. Besides, PrOT also yields a restricted Pareto front, which can be attributed to the difficulty of partitioning tasks based on preferences. Fine-grained divisions result in data insufficiency for each task, while coarse-grained divisions lead to multiple preference behaviors being grouped into
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single task, both of which can hurt the policy performance and diversity. In contrast to BC-Finetune and Prompt-MODT, our method explicitly learns set of policies with various preferences through MORI,, thereby ensuring policy diversity. Once the target preferences are accurately identified, we can generate policies with diverse behaviors to meet various target preferences. To verify the capability of our method in preference alignment, we show the differences between the adapted preferences obtained by our method and the real target preferences in Figure where we can observe strong consistency between the adapted preferences and the real ones, especially PDOA [MODF]. additionally present the performance, Pareto fronts and preference comparison on the D4MORL expert datasets in Appendix A.6.1 which consistent with the results in this section.
Hopper
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0f
45 Okg)
thef 84
51 PDGK [MORVS]
25
51. Be 50 6h
PSDA (MODF)
Adisptes Tirget
Figure The comparison between the real target preferences and the adapted preferences.
5.2 Constraint Satisfaction for Safe RL Tasks
OfflecSulCrrdev
Offinetul
10
10
Safdty Trnchold
Saftty
Sufityy Trrchhoi
Saloty
FROM (NO0F)
P024 PO24|NGRA (NGRvS]
Fromit MOOT
SC- Eeruue
CDT Orycle
Koma Corz. Target Theechol
Figure 4: The adapted policies' cost and utility each algorithm under various safety thresholds. Here, the utility is the normalized reward, since there is only one unconstrained objective in DSRL tasks. The points above the black dashed line represent the policies that violate the constraints.
Figure II in Appendix A.7 presents the Pareto fronts of MODF and MORvS, i.c., the expected costs and expected rewards under various preferences, for safe RL tasks, which demonstrates that MORL algorithms can learn a variety of policies that meet various safety thresholds. Then, the reward and cost of all algorithms tasks in Appendix [A.7 These results show that, even though the safety thresholds are inaccessible, PDOA [MODF] achieves relatively safe performance under various safety thresholds compared baseline
shown in Figure We also present the performance and Pareto fronts other
to other baselines, closely matching the oracle performance of the threshold-infomee CDT. Even with very tight safety thresholds, PDOA [MODF] can achieve constraint satisfaction or experience few constraint violations. Meanwhile, its reward performance is comparable to or even exceeds that of CDT. However, PDOA [MORvS] performs poorly on the DSRL datasets because MORvS requires accurate predictions of the target return for each preference, which is challenging due to the abundance of suboptimal trajectories the DSRL datasets. Additionally, BC-Finetune and MOOT,, which align behaviors without considering the constraints on constrained objectives, exhibit insufficient policy diversity and constraint violations in most environments.
5.3 Evaluation for Constrained MORL Tasks
The results on CMO datasets are shown in Figure 5 The CMO tasks involve more objectives than previous MORL and safe RL tasks, posing challenge in identifying and aligning behaviors.
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110
310
51
15
10
2133
115
107
210
115
30-
16
115
160
26
16
28
16
38
Safety Threchold
Safety Threshold
Safety Thredhold
Safety Threshold
PDDA
Threshol
Figure 5: The maximum cost, the average utility and Hypervolume over all targets with specific safety threshold.
This is because behaviors with various preferences increase exponentially as the number of objec- tives increases. We can observe that most environments, the performance BC-Finetune and Prompt-MODT shows low Hypervolume and weak correlation with the safety threshold, indicating that they cannot align with the desired behaviors and exhibit high policy diversity. Nevertheless, PDOA [MODF] approaches the oracle performance with high average utility, Hypervolume, and few constraint violations, which is consistent with the results presented Sections 5.1 and 5.2
5.4 Ablation Study
2.12
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Figure 6: The performance across different demonstration sizes (abbr. DS) in Figure (a)(b) and the performance under various conservatism parameters (abbr. CVaR) in Figure (c)(d).
In this section, we aim to figure out: 1) the impact of the quantity of demonstrations on adaptation performance, and 2) the influence of the conservatism parameter of Eq. (10) on safety performance. We conduct of ablation experiments for PDOA [MODF] on several MORL and safe RL tasks and present the results in Figure 6 In Figure (a),), as the demonstration size (DS) increases, our method achieves better average utility. Hypervolume for MORL tasks and higher reward for safe RL tasks. Nevertheless, even with a very small number of demonstrations (DS 16), the adapted policies generated by our method still exhibit sufficient diversity and safety. Figure (c) demonstrate that by increasing the conservatism parameters, we can further reduce constraint violations and ultimately achieve constraint satisfaction, which validates the effectiveness our conservatism mechanism in enhancing safety.

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6 Conclusion
In this paper, we present an offline adaptation framework Preference Distribution Offline Adaptation (PDOA) for constrained MORL problems where we assume no access to real target preferences or safety thresholds and only a few demonstrations with expected behaviors are available in our framework. For unconstrained MORL scenarios, we propose to 1) employ MORL methods to train set of preference-varying policies, and then 2) align the preferences of adapted policies with expected behaviors. Furthermore, we expand our framework to accommodate constraints on specific objectives by transforming constrained problems into unconstrained counterparts. Additionally, we introduce a conservatism mechanism for preference estimation constraint violations. Empirical results on MORL and safe RL tasks illustrate the capability of our framework in generating diverse policies aligning with expected behaviors and approach constraint satisfaction through conservative preference estimation.
constrained objectives to mitigate potential
Limitation The PDOA framework involves multiple steps of preference sampling and gradient updates, which can lead to additional computational burden and latency during deployment. Besides, although the manual design of preferences and safety thresholds is not necessary, the process of constructing demonstrations may still involve human expertise.
Acknowledgements
We gratefully acknowledge the support from the National Natural Science Foundation of China (No. 62076259, 62402252), the Fundamental and Applicational Research Funds of Guangdong Province (No. 2023A151501 the Fundamental Research Funds for the Central Universities Sun Yat-sen University, and the Pengcheng Laboratory Project (PCL2023A08, PCL2024Y02).
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A Appendix supplemental material
A.1 Connections and Differences to Other Fields
Multi-task RL While the constrained MORL setting we focus on can align with the multi-task framework by treating policy learning under various preferences or thresholds as distinct tasks, several key differences distinguish our study from previous multi-task RL settings: (1) One primary motivation of our work is to cireumvent the handerafted design of target preferences, whereas previous studies [Mitchell et al. 2021 Xu et al. 2022a] on multi-task RL mainly focus on policy generalization to new tasks. (2) We achieve offline adaptation by updating the target preference distribution rather than the policies themselves, which distinguishes our framework from offline meta-RL methods. This adaptation pipeline not only avoids potential performance degradation due to policy parameter shifts but also allows us to incorporate conservatism mitigate constraint violations. (3) Accurately identifying various preferences and constraints implied in demonstrations during adaptation is challenging as these demonstrations could come from the same dynamics and policies with similar preferences.
Multi-constraint RL Existing research on multi-constraint RL typically explores the correlation between multiple constraints from gradient perspectives (aao et al. 2024b, Kim et al. 2024), Some works [Guan et al. 2024b) attempt to meet different types of constraints simultaneously. In contrast, our approach, from the policy diversity perspective, aims to find appropriate policies for various safety requirements and thus places less focus on constraint correlation for specific threshold. Nevertheless, previous studies on multiple constraint RL will provide important insights into managing potential correlations between multiple objectives during preference-condiitonee policy learning, thereby improving overall performance.
Inverse RL Existing IRL methods [Arora and Doshi, 2021 typically assume no knowledge about the reward function and focus on learning reward functions from mere demonstrations through apprenticeship learning, maximum entropy optimization or adversarial learning. Some of these methods have been applied in MORL [Takayama and Arai [022] or safe RL (Malik et al. a [2021]. In contrast to these studies, our work assumes knowledge of the reward information different objectives and pays more attention to identifying the preferences of demonstrations during deployment than learning specifie decisive reward during training.
Bayesian RL
Bayesian RL (Ghavamzadeh et al. 2015) is widely used for promoting online exploration and dealing with uncertainty in model-based RL offline RL, while it serves cornerstone of our theoretical derivation, allowing us to incorporate prior preference information from datasets and infer the expected preferences by estimating the preference posterior based few demonstrations. Ghosh's work [Ghosh et al. 2022 is the most related Bayesian RL study that inspires approach. Nevertheless, it aims to reduce the dynamics uncertainty caused by limited offline samples, while our approach focuses on utilizing Bayesian inference to solve the uncertainty of the target preference distribution based few demonstrations.
Offline Imitation Learning Each adaptation can be viewed as the imitation a expert policy with certain preference. Therefore, offline Imitation Learning (IL) is potential approach to solving the problem by applying an off-the-shelf offline IL algorithm [Xu et al., 2022b Kim et al. 2022), which enables the combination of sub-optimal trajectories in the offline dataset with expert demonstrations provided by users to imitate expert behaviors. However, applying offline IL to our problem presents several challenges. We conduct comparative experiments in Appendix A.8 to further compare algorithms and illustrate these challenges.
A.2 Environments and Datasets Details
Environments and Datasets for Multi-objective RL We utilize the D4MORL dataset Zhu et al. 2023 collected from multi-objective MuJoCo environments by set of preference-varying policies [Xu et al.) [020]. We consider MuloCo tasks including HalfCheetah, Ant, Hopper, Walker2d, and Swimmer. Among them, the HalfCheetah, Walker2d, and Swimmer tasks involve
13

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conflicting objectives of running speed and energy saving. The Ant task includes two speed objectives in both the x and y axes, while the Hopper considers running and jumping objectives. For each task, we test algorithms on two types of datasets: Expert and Amateur, which are collected by pure expert policies and noise-injected expert policies, respectively.
Environments and Datasets for Safe RL We utilize the datasets in DSRL benchmark [Lu et al. 2023b] that are collected by a set of behavior policies trained under various safe thresholds. We select 8 Buulettafetyyynn tasks [Gronauer] [022] for safe RL experiments, which involve 4 agents (Ball, Car, Drone, Ant) and task goals (Run, Circle). In these tasks, the goal of the reward function is to navigate to target positions complete circuits as quickly as possible, while the costs are incurred when the agent enters risky areas.
Environments and Datasets for Constrained Multi-objective RL We develop set of CMORL tasks, namely CMO-Hopper, OMOO-Halfhheethh, CMO-Ant and -wim-e.mmer. These tasks are constructed based on the multi-objective MuJoCo environments (Xu et al. 2020) and augmented by an additional constraint on robotics' velocity, which is consistent with the constraint setting of Safety Gymnasium tasks in the DSRL benchmark. When the agent's moving velocity exceeds a specific value, it will receive 1 cost. To gather datasets for these tasks, we create a behavioral preference set and utilize TRPO+Lagrangian [Liu al. 2023b to train individual policies with the goal of maximizing utility under each preference in this set while accounting for a specified velocity constraint. The safety threshold of the velocity constraint is adjusted throughout the training process to encompass a range of potential safety thresholds. The details for each CMO task are shown in Table [ The replay buffers collected during the training of these policies constitute the CMO datasets. We present Pareto fronts of CMO datasets under different cost return intervals in Figure 7 illustrating that CMO datasets encompass wide range of behaviors catering for various preferences and safety thresholds.
Table 1: Details of each CMO task.
Details
CMO-Ant
CMO-Hopper
CMO-HalfCheetah
CMO-Swimmer
behavioral preference Set
[0.5, 0.5), [0.6, 0.4), (0.7, (0.8, 0.2), [0.9, 0.1), 0.0)
Cost function
Moving Velocity (cost=1 the velocity exceeds a specific value)
Threshold Range
250]
200]
Speed on X-axis and Y-axis
Moving speed and jumping height
Moving speed and energy consumption
Objectives
A.3
Construction of Training Set and Demonstration Set
(1) For MORL experiments in Section 5.1 each target preference w, is associated with a demon- stration set Bw,,, which contains M transition randomly
randiomlly sampled from K trajectories in D4MORL Expert datasets with behavioral preferences closest to the target preference Wg. (2) For safe RL experiments Section 5.2, each target safety threshold B3 is associated with a demonstration set E3, which contains M transitions randomly sampled from K trajectories in DSRL datasets with the highest utility among all safe trajectories (i.e., these trajectories' cumulative cost return less than 9). (3) For CMORL experiments in Section 5.3 each combination of target preference wy and safety threshold 3,y is associated with a demonstration set B,,,,,, which consists of M transitions randomly sampled from K trajectories in CMO datasets that (i) have highest utility among all safe trajectories and (ii) originate from the replay buffer of the behavior policy with preference W,- The unselected trajectories in datasets constitute the training set. our experiments, M 128 and K 2 by default.
Forr CoopttMODY which required trajectory segments as prompts during adaptation, we sample trajectory segment with M constitute the demonstration set.
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3.0cremgi10
berettlb63
1 $5.0
3henstg00.
berozs56n
bonddgt2
12A0enststitn
Figure 7: The reward vector distribution of CMO datasets under various safety thresholds.
A.4 Evaluation Metrics
We denote R(TG) as the estimated return vector of the policy aа adapted for target G in the target
set T.
Average Utility
For unconstrained scenarios, G Wg and average utility is caleulated by:
U
1
w B(Tww)) WT
Σ
(11)
For constrained scenarios, = (wgg 3). We denote TB, groups all target preference w, by safety threshold B. The average utility is function of Byy
B,)) E T as subset of 7 that
1
U(B
Σ
w/ ((
(12)
[Tg,
W,ETo,
This metric reflects the overall performance of the adapted policies across all target preferences.
Hypervolume We first consider the unconstrained settings and introduce the adapted Pareto set P that contains all adapted policies that are not dominated by any other adapted policy. Hypervolume measures the volume enclosed by the returns of policies in the adapted Pareto set P:
HV = / 1 (z))) Rm
HV=
(13)
where (P,, = (= B E P: P: otherwise. For constrained scenarios, we group all target preferences by safety threshold and report Hypervolume each group. The Hypervolume reflects not only the overall performance across all target preferences but also the diversity of the policies, as a high diversity of policies corresponds to a broad Pareto front and consequently high Hypervolume.
R(T)) and LH(P.))) equals if HPP) and 0
Sparsity, which measures the density of policies in the approximated Pareto set, also commonly used for evaluating MORL performance. A lower sparsity indicates denser Pareto front, which
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Algorithm Preference Distribution Offline Adaptation
1: ### Training Phase
2: Input: Offline dataset D
3: Train policy-conditioned policy T 8, w) or value Q(s, a, w) using MODF or PEDA
4: Approximate the prior preference distribution P))
5:
6: ### Adaptation Phase
7: Input: Demonstration set B, and conservatism parameter
8: Initialize (H, oI) based on P(w(DD
9: for each interaction do
10: Sample preference w from M(,, oI)
11: Update μ, through gradient descent (Eq. (7))
end for
13: if no constraint then
14:
w pl|
15: else
16:
Compute b based on Eq. (10)
17:
b.=b/lb
18:
end if
19:
Output: Policy A (.) for decision making
generally more desirable. However, the sparsity metric is not applicable in setting. This is because, given that the number of adapted policies is fixed, an increase utility and Hypervolume performance can result in worse sparsity metric. Moreover, better sparsity metrics encourage lower diversity of adapted policies, which diverges from our intended goal.
A.5 Implementation Details
The pseudocode for the training and adaptation process provided in Algorithm
T
Behavioral Preference Approximation Scheme in Constrained Settings In constrained settings, the vector reward is defined as F [r,, -c,] and dataset D is augmented D. For behavioral behavioral preferences for all transitions in
preferences in DD utilize + (T)]l trajectory т. Here, U(T) = RI.... Rs: CTaax Ci..., Cx Cx). where R; and C, represent the accumulations of the th reward and cost of т, respectively, and C. is the maximum of C; among all trajectories. The formulation of w aims to approximate the normal vector of the Pareto front that consists of (R), RN; -C Ci. Ci...,, -Ck)
Preference Distribution Offline Adaptation (PDOA) We utilize the policy and value function obtained by MODF and PEDA to calculate the TD reward and action likelihood reward in Eq. 77. For
MODF, except the state-action value function (s, a, w) Qi (s, a, w), ..., Qv(s, a, w) obtained during training, we additionally train a state value function V(s, w) Ez(alsww [Q (s, a, w)] to derive TD reward. As for the action likelihood reward, the action likelihood of the diffusion policy model is intractable but can be approximated as log # (a|s, w) = E,-MM.~~((.TT) (o.ooo)llaaaa a01 (Kang
et al. 2,24], where a is reconstruction of a' and a² is obtained by corrupting with noise For PEDA, which does not involve value functions, we disregard the TD reward when calculating the adaptation loss. The prior preference distribution ((w (D) in Eq. (7) is approximated with Gaussian distribution N ((HD. DD), where the expectation μuD and standard deviation op are estimated on behavioral preferences of the training dataset D. The weight 7 of the regularization term (I] 1)² in Eq.
set to 1.0.
During adaptation, we model the preference distribution using Gaussian model and perform gradient updates on this distribution according to Eq. (7). For each target, the number of gradient updates set to 1000, with 64 preferences sampled from the distribution for each gradient update. All samples the demonstration set are used for gradient updates within one batch. We use the Adam optimizer
with learning rate of 0.05. The conservatism weight in Eq. 10 is set 1.0 for MORL tasks
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and 0.7 for safe RL and CMORL tasks. The weight of the TD reward in Eq. 6 is set to 0.01 for PDOA [MODF].
MORL and Safe RL Algorithms For MODF, we use the original implementation in https: We remove the Regularization Weight Adaptation component in the original MODF since it requires additional online interactions during evaluation. We follow the default hyperparameters except for the regularization weight, which is set to 200 for MORL and CMORL tasks and 20 for safe RL tasks. For PEDA, we use the original implementation in lhttps://gi thubbb....uu......... com/ htmmbbitingzbt/PIl/
7/gi com/ cwwmciammaaiccaeeeeaeecceecaeeee aataaniiO4/PRRaa
PEDA utilizes linear regression model to predict target vector returns given target preferences. For D4MORI. datasets, it fits this model using Expert datasets. In DSRL and CMO datascts, which contain suboptimal samples, we construct a Pareto set that consists of all uear-undominated trajectories with a small tolerance (5%) and use it to fit the linear regression model. For Prompt-MODT, we implement based on the MODT algorithm in PEDA by incorporating prompts into the decision transformer. The target vectors predicted by the above linear regression model are used as the initialized return-to-ge for Prompt-MODT. Besides, to apply Prompt-MODE we need transform the multi-objective problem into multi-task problem, for which we divide trajectories with different behavioral preferences into separate tasks with preference interval of 0.05. For example, trajectories with behavior preferences ranging from [0.00, 1.00] to [0.05, 0.95] are classified as task 1, and trajectories with behavior preferences ranging from [0.05, 0.95) to [0.10, 0.90) classified as task 2. For BC-Finetune, we model the policy using a Gaussian model and employ behavioral cloning through MSE loss. During adaptation, behavior cloning is performed on the demonstration set with 0.01 learning rate and 1000 gradient update steps.
Computer Resources The training and testing were conducted on 1 NVIDIA GeForce RTX 3090 GPU. The testing utilizes 5 CPU threads to simultancously collect test data from multiple environments. The total time for training and testing does not exceed 10 hours. The memory usage for single run depends on the size of the dataset used, but generally does not exceed 10 GB.
A.6 Additional Results
A.6.1
Experimental Results on D4MORL Expert Datasets for MORL
Sunjorraaky
Avg Utintt
MO-Antv2
MO 50-Smmmmer122
Halfhhcchhhh Let
Hop
Naller2dd 1st
1.7
175
4,5
POGA (MODF))
PodA (ecrie))
Prapge stoT
PbdA (ooto))
Prompe Poo7
PODA (NODF))
KodA (Momd))
Prompe AGOOT
Sc-Rimetune
PDdA (MODF)
PODA (MORdS
Prompe 6007
SoDA (OORd))
Promie MoOT
Aug Utility
Hypervolume
Aug Utility Oracle
Hypervolume Oracle
Figure& 8: Average utility and Hypervolume performance of all algorithms D4MORL Expert datasets.
Saimmessspart S-opprt
lisspeneszet
sspert
135
00,05H022
20
50
12
20
obysdive
120 128 Al 105
objective
(MODF)
Poopp-OOR
Figure 9: Pareto fronts of different algorithms D4MORL Expert datasets. Each point represents the expected vector return of an adapted policy for a specific unknown target preference.
We present the average utility and Hypervolume performance, Pareto fronts, and the difference between real target preferences and adapted preferences the D4MORL Expert datasets in Figure 8
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Amn
HalChretan
Wnoper
2d
Ahype Prd en Onl
Resl Derper Port on DN0)
Real Trgge Phaff on DNI
Dea Terget Free on Chil
Best Birger Phrt ONT
Real To get Port Day!
Prdelaige:Prd
Figure 10: The comparison between real target preferences and adapted preferences on D4MORL. Expert datasets.
9 and TO respectively. In Figure 8 our method demonstrates overall competitive performance in terms of average utility and Hypervolume metrics. Figure iillsstraees that our method achieves broader Pareto front, indicating high diversity of adapted policies. Figure shows that our method can obtain expected behaviors due to the consistency between our adapted preferences and real target preferences. These results consistent with those obtained on the Amateur Datasets Section 5.1 which demonstrates that our framework achieves consistent advantages across datasets of varying quality.
A.7 Experimental Results on Additional DSRL Tasks for Safe RL
Figures T1 and 12 show the performance of MODF and MORvS under various target preferences, which demonstrate the capability of these MORL algorithms in obtaining policies that satisfy different safety thresholds. Figure 13 illustratess the normalized cost and reward for additional DSRL tasks, including CarCirele, DroneCirele, CarRun, and DroneRun. The results are consistent with those in Section 5.2] demonstrating that MORL methods can effectively learn set of policies that meet various safety thresholds, and that PDOA [MODF] can achieve very few constraint violations.
Numerrod Rovara
No Normazzed
Norma bed
homslood
Vorma
Figure 11: The normalized cost and normalized reward of policies with various preferences obtained by our framework.
Offineca Cedeeve
OffineDronCrddee
Offii-Gronduun-i
Nonn Nonnakeee pensed
264
hormal Cost
Nomma bed Cost
homalzzd Cost
Norma losd Cost
Figure 12: The normalized cost and normalized reward of policies with various preferences obtained by our framework on additional tasks.
A.8 Comparison with Offline Imitation Learning Baseline
Applying offline II. to our problem faces several challenges: 1) Offline II. requires complete policy training for each adaptation, which is resouree-intensive and time-consuming, 2) Our experiments
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Safety Tireshold
Safrty Thessoid
Safety Thredhald
Safety Threshatd
FDOA (KODF)
PD3A (NCR
Frompt MOOT
SC-Fnetune
COT Oracie
Nomaa Cost- lagget Threansld
The adapted policies' normalized cost and normalized reward of all algorithms under various safety thresholds additional tasks.
Figure 13:
involve limited number of demonstrations (128 transitions per target preference) compared the millions of samples in the offline dataset, leading to significant demo sufficiency and data imbalance.
We apply OIL baseline DWBC Xu al. 2022b) in MORL and safe RL experiments and present the results Figure 14 and 15 where we limit the number tested preferences to 10 in the D4MORL tasks because the original evaluation involves dozens of target preferences per task, and training policy for each target preference using DWBC would too time-consuming. MORL and safe RL environments, DWBC demonstrates unstable performance. It is competitive in tasks such as MO-Ant, MO-Swimmer, but performs poorly in other tasks, including MO-Walker22 even struggles learn effective policies in issues can be attributed to demo sufficiency and data imbalance. Additionally, DWBC experiences high constraint violations in most safe RL tasks, as it does incorporate safety considerations into its policy learning.
both
cases, such MO-Hopper and AntCircle. These
MO Antu2
MO Sulmmerr
HD HalCheebhh
MO Hee
MC Whller2d
PoRA (ocoary
rooK (MGRAS)
Pronget MCDT
aC/torune
DWicc
POXUA (MzzPry
2000 (McoRuy
Pronept Prompe-Mtat MOOT
Bic ac-roooon
Diiec.
Poil MoDDo
pars (MLL815)
Promopt -MDD
ac-oortue
OWiiCC
Ponce hezze9)
Prompe MODT
ac biceteebine
Dritc
pors HASDP)
parae (MORSS)
Pronget 4000
DwMicc
Avg Utility
Hypervolume
Avg Utility Oracle
Hypervolume Oracle
Figure 14: Comparative results with offline II. baseline on MORL. tasks.
offincrrdRuno
offineea
101
63.
Safety
PDDA (NOO]]
POSA (MDRv5)
Promp:-MODD
BC SC-Rmittne
DWBC
CD7 Oracie
Nomalized Cesti Threshol
Figure 15: Comparative results with offline IL baseline on safe tasks.
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TO
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MO arTEea unffor wut PLA
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(b) PDOA [MORvS]
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TD rouard
reved
TO rever
TD raverd
(c) PDOA [MODF]
hat
Pert
Prd)
(d) PDOA [MORvS]
Figure 16: The relationship between TD reward, action likelihood reward, and preference. Prefl represents the first dimension of preference.
A.9 Relationship between TD Reward, Action Likelihood Reward and Preference
For each target preference, traverse all possible adapted preferences with small interval and compute the corresponding TD reward and action likelihood reward. The results are presented in Figure [6] where observe that the adapted preferences corresponding to the highest TD reward and action likelihood reward align with the target preferences. Additionally, as constraints are relaxed, the preference weights allocated to the constrained targets decrease. This demonstrates that the TD reward and action likelihood reward in our algorithm are strongly consistent with the target preferences and safety thresholds.
A.10 Licenses
D4MORL dataset and PEDA code (Zuu al. 2023 The MIT License, https://githubb Con/bbiitinggbt/PDDA
Datasets and codes of DSRL, OSRL and FSRL Liu et al. 2023b]: : All datasets are
censed under the Creative Commons Attribution 4.0 License (CC BY 4.0), and code
is licensed under the Apache 2.0 License. https://github..c https://github... wttp:/hwww..omm/uuuuu....uu DSRL https///ww.aaatao/ggo/oo//ooo//a
MuloCo: Apache 2.0 License, http:://ggihub.cmmmoogglle--6
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A.11
Broader Impacts
Our research introduces novel framework for addressing constrained multi-objective reinforcement learning (CMORL), which is widely applicable to many real-world scenarios, such as autonomous driving, healthcare, where behavioral preferences and safety criteria are difficult to define precisely. These approaches liberate researchers from the labor required to align preferences and safety thresh- olds. Besides, the offiine training paradigm eliminates the expenses and dangers associated with online exploration. For instance, in autonomous driving, online interactions with the environment have the risk of accidents and injuries; however, our method can mitigate this risk by learning from pre-recorded driving dataset generated by safe and target behavior policies.
Nonetheless, our method may not be suitable for domains requiring rapid responses and frequent updates due to the additional computational load and latency caused by gradient updates during adaptation. Besides, providing personalized services with this framework necessitates certain amount of user data as demonstrations, raising concerns about privacy breaches and data misuse. Despite the risks and challenges mentioned, we believe that CMORL holds great promise for automating and enhancing sequential decision-making in highly impactful domains. Additional work required to make this framework robust enough for application in multi oulti-objective and safety-critical scenarios.
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Reviews:
[{"review_id": "1agmw6vVyt", "reviewer": "Reviewer_FywX", "summary": "The paper tackles the important problem of adapting multi-objective policies to diverse preferences and constraints at deployment. This work uses state-of-the-art multi-objective RL methods to learn a set of policies that can align with diverse preferences. At deployment time, it doesn't assume access to the explicit hand-crafted preferences but introduces an adaptation method that uses demos to infer the target preferences. Additionally, the authors formulate this method to take into account explicit safety constraints at deployment time, inferred using only the demonstrations, without any online interaction. The approach is tested extensively on standard multi-objective and safe RL benchmarks, and they show that it can achieve higher performance, incur lower costs, and generate more diverse policies in these environments.", "questions": "1. The method is based on settings where the total reward is a linear combination of preferences and individual rewards. How can this setting be adapted to settings where we have access only to the total reward and demos and not the individual components? \n2. In the evaluation metrics, I would be curious to know why is the hypervolume and therefore, the diversity in the policies important. For the baselines, we observe that the policies with low hypervolume still have considerably close performance to this work in terms of utility and cost. A paragraph along these lines would allow a broader audience to understand the significance of these experiments and results.\n3. In certain environments, despite violating constraints, the returns are high, which indicates that the cost and the rewards are independent of each other. This is slightly confusing and I would appreciate some clarification in this respect.\n4. In Figure 6, it would be nice to analyze why higher demos incur a higher cost.", "limitations": "1. The method assumes access to the preferences at training time, which might not be practical for real-world settings, where the individual objectives and the preference distribution are unknown. This could be the reason that the method outperforms the prompt-MODT baseline i.e. the error introduced due to implicitly modeling the preferences, and not having access to the target distribution could potentially decrease the effectiveness of PDOA.\n2. The authors mention that the adaptation step is not real-time, which makes it difficult to transfer this system to real-world RL systems such as LLMs and robots.\n3. The evaluation is limited to locomotion environments, so, I suggest the authors include a discussion on the implications of the method and evaluation towards adaptation and safety in real-world RL problems.", "rating": 7, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The paper tackles an important problem of adaptation in multi-objective and safe RL. The intuition of the overall method is well understood, the framework and the parameters are mentioned, and the results are shown over the standard environments.\n2. The paper is well organized and presents a clear background of the past work in multi-objective RL. However, it would be nice to see a clearer distinction between the past approaches (PEDA etc.) used and changes (if any) made by the authors in this paper, for phase 1 of the methodology.\n3. Past work assumed access to hand-crafted preferences or online interactions to infer the preferences at deployment time. However, this work bypasses that by using a Bayesian framework to infer the preference distribution at deployment time using a set of demos explaining the preferred behavior. This is a more practical and scalable approach to adapting policies at test time.\n4. This method introduces an adaptation framework to infer the distribution of preferences from demonstrations. The authors lay out the theoretical and practical details for this step, including replacing the intractable Bayesian inference with a TD-error-based approximation from past literature.\n5. The introduced method is generalized to include safety constraints in the RL agent. This transforms the constrained RL problem, into an unconstrained multi-objective RL setting, which is compatible with the methods introduced in this work. Further, to ensure that the given approximation doesn't lead to excessive safety violations the authors use a CVaR-based objective, to always overestimate the constraints in case of uncertainty due to low demos.\n6. The authors demonstrate the effectiveness of their approach in several multi-objective and constrained simulation environments. The paper provides ablations to compare the effect of some hyperparameters and training methods on the efficacy of the method.", "weaknesses": "1. At training time, the method assumes access to the explicit preferences and demonstrations responding to those preferences. However, in practical settings, this information is not available even at training time, and the preferences and their clusters have to be learned in an unsupervised / self-supervised setting. I would be curious to know what the authors think about the effectiveness of this approach to learn the preferences and the policies in an end2end framework.\n2. I would recommend the authors to present a clear distinction between the past work, and the approach finally used in this work to generate the multi-objective policies. In this current presentation, it is slightly confusing to understand the particular contributions/adaptations of past work  to incorporate this with the posterior approximation framework. A pseudocode explaining the entire algorithm would make the method clearer to the readers.\n3. In the background, it would be nice to see some discussion contrasting the work in multi-objective adaptation to inverse RL, because in the introduction the authors mention - “it is more natural to infer expected behaviors through a few demos that implicitly indicate….” Comparing this to the approaches in inverse RL, and further, in Bayesian RL would be very useful to highlight the contributions. \n4. Under expert demos, the prompt-MODT baseline performs comparably to the methods introduced in this work. I would recommend the authors provide a wider discussion of the effectiveness of explicitly modeling human preferences using the adaptation module and if using the distributional Bayesian approach makes it robust to noisy samples.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for all the valuable comments. Please refer to the point-to-point responses below.\n\n**W1: Unavailable access to the explicit preferences**\n\nWe agree that unavailable access to preference labels is indeed a problem in real-world MORL applications. Some unsupervised techniques, such as clustering methods or contrastive learning, might help address this issue. In our paper, we adopt a simple yet effective solution proposed by MODF, which approximates the preference label of each trajectory with its normalized return vector ($R/|R|$) (see Appendix A.5). In our safe RL and CMORL experiments, where preference labels are unavailable, this simple solution leads to satisfactory performance.\n\nMoreover, our approach has the potential to promote preference learning when real labels are unavailable. Specifically, one can use the roughly approximate preference labels to train preference-conditioned models and then incorporate them into our framework to infer more precise preference labels for unlabeled trajectories in the dataset.\n\n\n\n**W2: Distinction between past work and ours, and pseudocode**\n\nBriefly, this paper studies a new and more realistic MORL problem (i.e., generating the expected behaviors without access to target preference) that differs from previous works. Our main contribution is a flexible framework to solve this new problem, rather than a new MORL method paralleled to MODF and PEDA. Specifically, existing MORL methods can be easily incorporated into our framework once they provide preference-conditioned policies or values, enabling them to solve this new problem that the original methods cannot. In our paper, we use the original implementation of MODF and PEDA without change, except for removing the RWA component of MODF due to its online interactions.\n\nWe will add pseudocode in a future version to improve understanding.\n\n\n\n**W3: Association with Inverse RL and Bayesian RL**\n\nWe appreciate the reviewer highlighting these connections. Preference inference is similar to identifying the decisive rewards of demonstrations, which is also the goal of IRL. Unlike traditional IRL methods, our work assumes a certain reward information and focuses on identifying preferences during deployment rather than learning decisive rewards during training.\n\nBayesian RL is fundamental to our theoretical derivation and explored in many RL sub-fields. While most studies focus on enhancing online exploration and managing uncertainty in model-based or offline RL, our approach employs Bayesian inference to address the uncertainty of the target preference distribution using a few demonstrations.\n\nWe will include more detailed discussions in the future version.\n\n\n\n**W4: Comparison to prompt-based methods**\n\nFirst, explicit preference modeling allows us to incorporate safety considerations into the MORL to enhance safety, while prompt-based methods lack safety guarantees and perform poorly in safe RL tasks. Additionally, explicit preference modeling allows users to verify the inferred preferences, thereby improving reliability. Besides, since prompt-based methods are designed for multi-task RL, they require users to spend extra effort transforming MORL datasets into multiple task datasets (see Appendix A.5), whereas our approach doesn't. Moreover, high noise in samples can be reflected as high variance in the inferred distribution, which can then be utilized to promote constraint adherence.\n\n\n\n**Q1: Access to only demos' scalarized reward, not vector reward**\n\nOnly the demos' scalarized utility may provides limited information for policy learning as utilities under different preferences can't be directly compared. This makes evaluating each trajectory's performance difficult, turning the problem into unsupervised RL. In this case, a potential solution is to cluster trajectories and imitate those most similar to the given demonstrations.\n\n**Q2: Importance of hypervolume and diversity as metrics**\n\nThe utility metric in our paper measures average utility across target preferences. But it may not accurately reflect overall performance if reward scales vary greatly. In contrast, the hypervolume metric measures the volume enclosed by the learned policies' returns, directly reflecting Pareto front performance, which is crucial in MORL research. Hypervolume is also less sensitive to reward scaling and is a common metric in previous MORL studies, facilitating fair comparisons.\n\n\n\n**Q3: Relationship between return and cost**\n\nCost and reward generally correlate positively, so high constraint violations (i.e., high costs) often come with high rewards. However, poorly learned policies can lead to both high costs and low rewards.\n\n**Q4: Connection between the number of demos and cost in Figure 6**\n\nMore demonstrations reduce uncertainty (variance of adapted preference distribution) by lessening the entropy item's effect in Eq. (7), which then weakens the conservatism estimation (Eq. (10)). Thus, both cost and reward increase.\n\n\n\n**L1: Unavailable access to explicit preferences**\n\nRelated discussions are provided in response to W1.\n\n**L2: Real-Time adaptation**\n\nWe think that frequent preference switching isn't very common in real-world applications. Additionally, the time bottleneck is more likely the collection of new demonstrations rather than the inference. Besides, using fewer gradient update steps and simplifying the network structure could improve inference speed.\n\n**L3: Discussion on real-World RL problems**\n\nWe detail the application of our approach to real-world RL problems in Appendix A.10. We emphasize that designing target preferences or safety thresholds is a complex task requiring extensive trial and error in real-world scenarios.\n\nFurthermore, previous MORL methods that could be part of our framework have been tested in various environments like discrete grid-world and game tasks. Therefore, we believe our approach is promising for diverse real-world tasks beyond locomotion environments.", "claims_and_evidence": "", "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": "", "extra_scores": {}}, {"review_id": "VBPxdKIhtR", "reviewer": "Reviewer_ZqLH", "summary": "This paper addresses the issue of handcrafted target preferences in multi-objective RL (MORL) by proposing an offline adaptation framework called Preference Distribution Offline Adaptation (PDOA), which implicitly learns the preferences from a small number of demonstrations. Specifically, PDOA involves two steps: (i) It learns a set of policies for various preferences during training using an off-the-shelf MORAL algorithm; (ii) It then adapts a distribution of target preferences based on the demonstrations at deployment. To update the posterior of target preferences in a tractable manner, PDOA adopts multiple approximation schemes for both unconstrained and constrained settings. Moreover, in the constrained setting, to address the discrepancy between the true preference and the estimated one, PDOA also proposes to use a conservative estimate with the help of CVaR. The PDOA is evaluated on multiple MOD4RL locomotion tasks and has strong performance in terms of average utility and hypervolume. Empirical studies on the number of demonstrations and the conservatism parameter are also provided.", "questions": "Please see the comments above. Some additional questions:\n- How many trajectories (in the demonstration set) are needed for target preference adaptation in the main experiments (Figures 1-2)? \n- In Equation 5, during the preference estimation phase, the dataset $\\mathcal{D}$ only takes part in the prior $P(\\omega| \\mathcal{D})$. Under PDOA, it could be possible to leverage the information from $\\mathcal{D}$ to further improve the accuracy of the target preference. Can the authors comment on this?", "limitations": "The paper discusses one limitation about the need for human expertise in constructing demonstrations in Section 6.", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "- This paper identifies and addresses the issue of target preference estimation by offline preference adaptation, which is a novel setting in the literature of MORL.\n- The idea of rethinking target preferences from an Bayesian inference perspective is quite interesting. The overall approach looks reasonable (despite some concerns listed below).\n- The experiments are done on multiple D4MORL tasks, and the results in terms of utility and hypervolume are quite promising. \n- The ablation studies are quite helpful in understanding the robustness of PDOA.", "weaknesses": "- One issue is the lack of stronger offline imitation learning baselines. If we already have a number of demonstrations of the target preferences at test time, then one reasonable solution is to view this as a single-objective problem and then apply an off-the-shelf offline imitation learning (IL) algorithm with these demonstrations, such as DWBC [Xu et al., 2022] and DemoDICE [Kim et al., 2022], which both focus on offline imitation with a small number of expert demonstrations along with other sub-optimal trajectories. In the setting of PDOA, one can simply do offline IL by using $\\mathcal{B}_\\omega$ as the expert demonstrations and $\\mathcal{D}$ as the sub-optimal samples.\n- Another concern is on approximation of the posterior in (6). While I can get the intuition that in-distribution samples tend to have higher $r^{TD}$, the surrogate in (6) appears to be quite heuristic and not very principled. Specifically, the $\\pi^*$ in the original posterior expression could be different from the policy (whose Q and V are used in Equation 6) learned by MORL at the first stage. More theoretical justification of this approximation is needed.  \n- For the constrained setting, there is an additional parameter $\\alpha$ to determine to strike a balance between constraint violation and achieved utility. However, my concern is that $\\alpha$ is a parameter to be used at test time, and hence there is very little one can do in terms of parameter tuning. While Figure 6 did provide a study on the influence of $\\alpha$, we can see that this value does matter a lot in the balance between constraint violation and utility. As a result, this could make PDOA less attractive in practice.\n\n[Xu et al., 2022] Haoran Xu, Xianyuan Zhan, Honglei Yin, and Huiling Qin, “Discriminator-Weighted Offline Imitation Learning from Suboptimal Demonstrations,” ICML 2022.\n\n[Kim et al., 2022] Geon-Hyeong Kim, Seokin Seo, Jongmin Lee, Wonseok Jeon, HyeongJoo Hwang, Hongseok Yang, and Kee-Eung Kim, “DemoDICE: Offline Imitation Learning with Supplementary Imperfect Demonstrations,” ICLR 2022.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for all the valuable comments. Please refer to the point-to-point responses below.\n\n**W1: Lack of offline IL baselines**\n\nApplying offline IL to our problem faces several challenges: 1) Offline IL requires complete policy training for each adaptation, which is resource-intensive and time-consuming. 2) Our experiments involve a limited number of demonstrations (128 transitions per target preference) compared to the millions of samples in the offline dataset, leading to significant demo sufficiency and data imbalance.\n\nNevertheless, we still apply an OIL baseline DWBC [1] in our MORL and safe RL experiments and present the results in the PDF attached to the global response. We use the same evaluation protocol as in the original study, except that we limite the number of tested preferences to 10 in the D4MORL tasks. This limitation is necessary because the original evaluation involves dozens of target preferences per task, and training a policy for each target preference using DWBC would be too time-consuming.\n\nIn both MORL and safe RL environments, DWBC demonstrates unstable performance. It is competitive in tasks such as MO-Ant, MO-Swimmer, and CarCircle, but performs poorly in other tasks, including MO-Walker2d, and DroneRun. It even struggles to learn effective policies in some cases, such as MO-Hopper and AntCircle. These issues can be attributed to demo sufficiency and data imbalance. Additionally, DWBC experiences high constraint violations in most safe RL tasks, as it does not incorporate safety considerations into its policy learning. \n\nFinally, we would discuss the related works and consider to supplement this results in the future version.\n\n\n\n**W2: Justification of TD-reward surrogate in Eq. (6) and discrepancy between the theoretical optimal policy and the one learned by MORL**\n\nAdmittedly, the use of TD-error approximation from Ghost's paper [2] is heuristic and based on empirical observations (as shown by the consistency of the TD term and real preference in Figure 14 of Appendix A.9). The related analysis involves the generalization of Q-value neural networks and its relationship to dynamics uncertainty, which makes it extremely complex. Alternative methods like model-based approaches or DICE methods could potentially offer more explicit dynamics modeling and theoretical insights, though they would also complicate the overall approach. Nevertheless, exploring these alternatives could provide more reasonable solutions and is a direction for future research.\n\nRegarding the discrepancy between the learned policy $\\pi$ and the optimal policy $\\pi^*$, it is evident that the KL divergence between the real posterior and the approximate one in Eq. (5) is bounded by the KL divergence between the policies, state distributions, and dynamics in the real and empirical environments, i.e., \n$$\nD_{KL}(\\hat P(\\omega|B,D), P(w|B,D))\\leq E_{\\hat\\pi,\\hat M}[D_{KL}(d_{\\hat\\pi}(s), d_{\\pi^*}(s))+D_{KL}(\\hat \\pi(a|s),\\pi^*(a|s))+D_{KL}(\\hat P(s',r|s,a),P(s',r|s,a))]+K.\n$$\nTherefore, as the learned policy approaches the optimal policy, the approximation gap decreases. However, the analysis of policy optimality for diffusion-based regularized methods in MODF and supervised RL methods in PEDA is complex and limited in the related works (as far as we know). Thus, we leave a detailed theoretical analysis for future research.\n\nBesides, we use the 'optimal policy' just as a theoretical bridge to simplify the analysis. Despite this discrepancy, our approach can still achieves meaningful adaptation because what we did is to select a well-chosen preference that ensures the learned policy’s behavior with this preference closely aligns with the demonstrations. Practically, this process does not involve the policy optimality directly.\n\n\n\n**W3: Conservative parameter $\\alpha$**\n\nFirst, since the parameter $\\alpha$ is used only in the deployment phase and each adaptation involves relatively few samples, fine-tuning $\\alpha$ is manageable. This can be accomplished with a few iterations of adaptation, which is feasible in many real-world applications.\n\nMoreover, Figure 6 demonstrates that our approach maintains relatively few constraint violations even when the conservatism mechanism is removed (i.e., $\\alpha=1$). This is because the equivalence relationship between constraint RL and MORL is key to solving constraint problems, while conservatism with $\\alpha$ serves as an enhancement based on this equivalence. Thus, a roughly designed $\\alpha$ will not significantly undermine our approach.\n\n**Q1: Number of trajectories in the demonstration set**\n\nWe select 2 trajectories from the original dataset and then randomly sample 128 transitions from these trajectories to construct a demonstration set for each target preference or safety threshold. For further details, please see Appendix A.3.\n\n\n\n**Q2: Potential Improvement from Extended Utilization of Dataset $D$**\n\nExcept for $P(\\omega|D)$, dataset $D$ also appears in the term $P(B_{\\omega_g}|\\omega,D)$ in Eq. (5), which is approximated using policy and dynamics estimation. This means that $D$ not only provides prior preference distribution information but also plays a role in calculating $r^{TD}_\\omega$ and $\\log \\pi$ in adaptation (i.e., Eq. (7)), as it is required when learning preference-conditioned models during the first phase.\n\nNevertheless, I agree that further leveraging this information is possible. For instance, measuring the similarity between demonstrations and samples in $D$ somehow could provide additional insights for better inference.\n\n[1]. Xu, H., Zhan, X., Yin, H., & Qin, H.. Discriminator-weighted offline imitation learning from suboptimal demonstrations. ICML 2022.\n\n[2]. Ghosh, D., Ajay, A., Agrawal, P., & Levine, S.. Offline rl policies should be trained to be adaptive. ICML 2022.", "claims_and_evidence": "", "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": "", "extra_scores": {}}, {"review_id": "KD7NcNFgGL", "reviewer": "Reviewer_58tv", "summary": "The paper presents a new multi-objective RL setup to learn a policy offline that can adapt to unknown target preference online, utilizing posterior estimates of the true target preference.", "questions": "For Eq 5, can the author comment on -- what is the estimation quality of the target preference policy if the sampling policy pi-hat-star-w is sub-optimal? I can break this question down to two parts:\n- How does the sub-optimality of the approximate policy to optimal policy affect the estimation of w?\n- How does the estimation quality of w affect the convergence of the approximate policy to the true optimal policy?", "limitations": "The authors addressed the limitation.", "rating": 6, "confidence": 3, "soundness": 4, "presentation": 4, "contribution": 3, "strengths": "1. The paper is very clearly written.\n2. The base policy is reasonable (decision transformer and diffusion policy).\n3. Experiment and figures are easy to follow.\n4. The methodology is built on solid prior work and the extensions are easy to understand.", "weaknesses": "After carefully thinking through this setup, I'm a bit worried about the core contribution of this paper. \n\nThere are several major challenges to offline learning of CMO-MDP:\n1. Policy learning conditioned on preference vector (solved by previous works and used in this paper) (MODF, MORvS)\n2. Trajectory distributions shift under the optimal policy and approximate policy, leading to failures of estimating preference vector w (solved by [Ghosh et al., Hong et al., 2022], Eq 6, used in this paper)\n3. Preference vector online estimation (through posterior update) (Eq 5) (this is a straightforward application), and the actual update is Eq 7.\n\nIt seems to me that the paper's core contribution is:\n1. Proposed a new problem.\n2. Proposed a good preference target vector estimation (Eq 7).\n3. Cast constrained problem as unconstrained and added a conservative estimate to the preference vector so that constraints are not violated during adaptation.\n\nI'm not fully able to determine how significant these contributions are.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for all the valuable comments. Please refer to the point-to-point responses below.\n\n**W1: About contribution**\n\nFirst, we would like to clarify that our primary contribution is not to develop a new MORL algorithm parallel to MODF or MORvS but to propose a flexible and minimalist framework designed to accommodate existing MORL algorithms and address new problems that the original algorithms cannot solve.\n\nRegarding the approximation technique in Eq. (6), we consider it more of an effective and replaceable trick rather than a critical component of the work. Because, there are several methods that could fulfill this role, such as explicitly modeling dynamics and stationary distributions through model-based methods or DICE techniques. We selected Ghosh's method due to its simplicity and effectiveness, as it does not require additional mechanisms that could complicate our framework and hinder its generalization.\n\nFurthermore, while the Bayesian formulation is intuitive, its application to MORL adaptation problems is relatively novel. It serves as the foundation of our solution and offers a new perspective for MORL research. Finally, we emphasize the significance of incorporating safe RL into our framework. The equivalence relation we propose is not only intuitive but also provides a unified perspective on both safe RL and MORL.\n\n\n\n**About 'optimal policy'**\n\nObtaining and evaluating the real optimal policy is challenging, especially in an offline setting where the quality of the learned policies is significantly influenced by the dataset. We use the term 'optimal policy' as a theoretical bridge to bypass the suboptimality of the learned policy and simplify the analysis. Despite this discrepancy, our approach achieves meaningful adaptation. This is because, in practice, we select a well-chosen preference that ensures the learned policy’s behavior with this preference closely aligns with the demonstrations, and the dynamics estimation based on these demonstrations remains relatively accurate. \n\n**How does the sub-optimality of the approximate policy to optimal policy affect the estimation of w?**\n\nWe can easily find that the KL divergence between the real posterior $P(\\omega|B,D)$ and the approximate one $\\hat P(\\omega|B,D)$ in Eq. (5) is bounded by the KL divergence between the policy, state distribution, and dynamics in the real environment and their empirical counterparts. i.e., \n$$\nD_{KL}(\\hat P(\\omega|B,D), P(w|B,D))\\leq E_{\\hat\\pi,\\hat M}[D_{KL}(d_{\\hat\\pi}(s), d_{\\pi^*}(s))+D_{KL}(\\hat \\pi(a|s),\\pi^*(a|s))+D_{KL}(\\hat P(s',r|s,a),P(s',r|s,a))]+K.\n$$\nThus, if the learned policies deviate significantly from the optimal policies, the estimation of $\\omega$ will be adversely affected.\n\n**How does the estimation quality of w affect the convergence of the approximate policy to the true optimal policy?**\n\nThe adapted preference $\\omega$ does not involve in policy training but still impacts the performance discrepancy between the adopted policy and the optimal policy. Even if we could obtain optimal policies for all preferences, poor performance could still arise if the predicted target preference deviates significantly from the actual one. This is because a policy might perform well under the predicted preference but diverge from the optimal policies with the real preference. \n\n \n\n[1]. Ghosh, D., Ajay, A., Agrawal, P., & Levine, S. (2022, June). Offline rl policies should be trained to be adaptive. In *International Conference on Machine Learning* (pp. 7513-7530). PMLR.", "claims_and_evidence": "", "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": "", "extra_scores": {}}, {"review_id": "t9fqQC1Oyp", "reviewer": "Reviewer_TEUx", "summary": "This paper presents a novel framework for multi-objective RL  that eliminates the need for handcrafted target preferences. Instead, it uses demonstrations to implicitly indicate the preferences of expected policies. The proposed offline adaptation framework can also handle safety-critical objectives by utilizing safe demonstrations, even when safety thresholds are unknown. The authors provide empirical results showing that the framework effectively infers policies that align with real preferences and meet the constraints implied by the demonstrations.", "questions": "(1) Preference is closely related to the reward function definition, and correlation among reward functions will result in preference calculation issues. For example, what if $r_1 = 0.5 r_2 = 0.2 r_3$, and $r_4$ is independent to $r_1$? In this setting, we would get a small preference mismatch score between two demonstrations even if they have significant differences in the reward returns for $r_4$. Do you have any methods to deal with this?\n\n(2) In section 4.2, the first step of your method is to learn a set of policies that respond to various preferences during training. How do you ensure that the learned policy is subject to specific preferences?\n\n(3) Based on the description in section 4.3, are High-reward-high-cost and low-reward-low-cost demonstrations categorized as similar behaviors?\n\n(4) How does the proposed method perform in other DSRL datasets/tasks such as Car-Circle and Drone-Circle?\n\n(5) Where are CDT results discussed in section 5.2? I did not them in Figures 3 and 4.\n\n(6) How do your method and problem formulation relate to multi-constraint safe RL since multiple constraints can also be viewed as multiple objectives? Some related works:\n\n[1] Kim, D., Lee, K., & Oh, S. (2024). Trust region-based safe distributional reinforcement learning for multiple constraints. Advances in neural information processing systems, 36.\n\n[2] Yao, Y., Liu, Z., Cen, Z., Huang, P., Zhang, T., Yu, W., & Zhao, D. (2023). Gradient Shaping for Multi-Constraint Safe Reinforcement Learning. arXiv preprint arXiv:2312.15127.\n\n[3] Guan, J., Shen, L., Zhou, A., Li, L., Hu, H., He, X., ... & Jiang, C. (2024). POCE: Primal Policy Optimization with Conservative Estimation for Multi-constraint Offline Reinforcement Learning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (pp. 26243-26253).", "limitations": "Yes, the authors addressed the limitations.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "(1) Interesting topics: Developing a framework for multi-objective reinforcement learning that does not rely on handcrafted target preferences is very interesting and potentially useful for real-world applications. Additionally, the framework uses demonstrations to implicitly indicate the preferences of expected policies, which can also be extended to meet constraints on safety-critical objectives using safe demonstrations.\n\n(2) Extensive experiment evaluation: The authors provided extensive experiment results including those on offline safe RL benchmark, offline RL benchmark, and multi-objective RL benchmark. These results show the flexibility and effectiveness of the proposed method.", "weaknesses": "(1) Preference is closely related to the reward function definition. How does this definition compare to other metrics such as the ones based on the states/state-action/latent variable distribution? For some tasks, there exists some correlation between reward functions, and this will potentially affect the preference estimation results.\n\nFor other potential weaknesses, please see my questions.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for all the valuable comments. Please refer to the point-to-point responses below.\n\n**W1 & Q1: Impact of reward correlation on preference match**\n\nWe might not fully understand the reviewer's concern about reward correlation, so we would appreciate further clarification if we have misunderstood. The concern seems to be that two policies with similar preferences might behave differently on one objective and thus generate different demonstrations because their preferences assign low weights to this particular objective.\n\nNevertheless, our approach does not suffer from this issue because practically it matches a demonstration to a specific preference based on its behavioral similarity to the learned policies (as indicated by the item $\\log \\hat{\\pi}^*_{\\omega}(a_t|s_t,\\omega)$ in Eq. (7)), rather than directly comparing the real preferences of demonstrations to those of trajectories in the dataset. As a result, even if two demonstrations are generated by policies with similar preferences, they will lead to distinct behaviors within our framework. \n\n\n\n**Q2: How ensure the learned policy to be subject to preferences**\n\nThe policy with a specific preference is expected to achieve high scalar utility, which is a linear combination of the preference weights and multiple rewards in our work. To accomplish this, MODF estimates the value vector $\\boldsymbol{Q}(s,a,\\omega)$ under different preferences and updates the policies to maximize $\\omega \\boldsymbol{Q}^T$. In contrast, PEDA falls into the return-conditioned paradigm, where it estimates the return vectors of expert policies for each preference and uses both the preference labels and these return vectors as decision conditions during behavior cloning. This approach enables it to approximate the expert's performance for each preference by conditioning on the specific preference and the predicted expert return vector.\n\n\n\n**Q3. Difference between High-reward-high-cost and low-reward-low-cost demonstrations**\n\nHigh-reward-high-cost demonstrations are generated by policies with a high preference weight on rewards and a low preference weight on constrained objectives (i.e., $r=-c$). Conversely, low-reward-low-cost demonstrations are generated by policies with the opposite preference (low weight on rewards and high weight on constrained objectives). Thus, these demonstrations should be associated with completely different behaviors.\n\n**Q4. Performance on other DSRL tasks**\n\nFigure 13 illustrates the results on additional DSRL tasks, including CarCircle, DroneCircle, CarRun, and DroneRun. The results are consistent with those in Section 5.2, showing that our method achieves fewer constraint violations and higher rewards compared to baselines and approaches the CDT oracle's performance.\n\n**Q5. Lack of CDT results in Figure 4**\n\nWe appreciate the reviewer pointing out this issue. In fact, the lines labeled 'MODF oracle' in Figure 4 and Figure 13 represent the performance of CDT. We will correct these legends in the future version.\n\n\n\n**Q6. Connection to multiple constraint setting**\n\nAs discussed in Section 4.3, multiple constraints can be viewed as additional rewards. This approach allows the original constraint problem to be equivalently converted into an MORL problem, which can then be solved through offline MORL adaptation by assigning appropriate preference weights to these constrained objectives.\n\nExisting research on multi-constraint RL typically explores the correlation between multiple constraints from gradient perspectives [1,2]. Some works [3] attempt to meet different types of constraints simultaneously. In contrast, our approach, from the policy diversity perspective, aims to find appropriate policies for various safety requirements and thus places less focus on constraint correlation for a specific threshold. Nevertheless, previous studies on multiple constraint RL will provide important insights into managing potential correlations between multiple objectives during preference-conditioned policy learning, thereby improving overall performance.\n\nAdditionally, we will supplement the related studies and discussions in our future version.\n\n\n\n[1] Kim, D., Lee, K., & Oh, S.. Trust region-based safe distributional reinforcement learning for multiple constraints. NeurIPS 2024.\n\n[2] Yao, Y., Liu, Z., Cen, Z., Huang, P., Zhang, T., Yu, W., & Zhao, D.. Gradient Shaping for Multi-Constraint Safe Reinforcement Learning. L4DC 2024.\n\n[3] Guan, J., Shen, L., Zhou, A., Li, L., Hu, H., He, X., ... & Jiang, C.. POCE: Primal Policy Optimization with Conservative Estimation for Multi-constraint Offline Reinforcement Learning. CVPR 2024.", "claims_and_evidence": "", "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": "", "extra_scores": {}}]

Author rebuttal:
We appreciate all the valuable comments from the reviewers. We have provided point-to-point responses to each reviewer's questions and will revise our manuscript according to their suggestions.

Meta-review: The paper studies a well-motivated, significant problem (multi-objective reinforcement learning) and proposes an offline adaptation approach that does not require preferences between objectives to be indicated during deployment time (instead they are inferred from offline demonstrations).
The reviewers agreed the proposed approach is technically sound, novel, and the empirical evaluations and ablations convincingly show the merits of the proposal. During the reviewer-author discussion, the authors clarified several weaknesses pointed out by the reviewers; incorporating them into a revision will substantially strengthen the paper.
Decision: Accept (poster)