arxiv: 2604.24532 · v1 · submitted 2026-04-27 · 💻 cs.LG

Recognition: unknown

A Reward-Free Viewpoint on Multi-Objective Reinforcement Learning

Ying-Tu Chen , Wei Hung , Bing-Shu Wu , Zhang-Wei Hong , Ping-Chun Hsieh

Authors on Pith no claims yet

Pith reviewed 2026-05-08 03:59 UTC · model grok-4.3

classification 💻 cs.LG

keywords multi-objective reinforcement learningreward-free reinforcement learningauxiliary taskpreference-guided explorationpolicy adaptation

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The pith

Adapting reward-free RL as an auxiliary task improves multi-objective policy learning across user preferences.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes treating the reward-free reinforcement learning objective as an auxiliary training signal for multi-objective reinforcement learning. This lets a single policy network share knowledge more effectively when user preferences are unknown or vary at test time. The authors adapt an existing RFRL algorithm and add a preference-guided exploration strategy to focus learning on relevant environment regions. Experiments across multiple MO-Gymnasium benchmarks show the combined method beats prior MORL approaches in both final performance and sample efficiency.

Core claim

By using the RFRL training objective as an auxiliary task and introducing preference-guided exploration, the adapted algorithm learns policies that generalize across preference vectors more effectively than methods that condition only on the given multi-objective reward function.

What carries the argument

The RFRL training objective employed as an auxiliary task together with a preference-guided exploration strategy inside the MORL training loop.

Load-bearing premise

That adding the RFRL auxiliary objective will produce useful knowledge sharing without creating instabilities or biases that hurt the primary multi-objective objective.

What would settle it

Direct experiments on the same MO-Gymnasium tasks showing that the proposed method yields no improvement or worse performance and data efficiency than standard preference-conditioned MORL baselines.

Figures

Figures reproduced from arXiv: 2604.24532 by Bing-Shu Wu, Ping-Chun Hsieh, Wei Hung, Ying-Tu Chen, Zhang-Wei Hong.

**Figure 1.** Figure 1: A motivating experiment on Deep Sea Treasure. view at source ↗

**Figure 2.** Figure 2: Evaluation of MORL-FB and several MORL benchmark algorithms on diverse continuous view at source ↗

**Figure 3.** Figure 3: Evaluation of MORL-FB and several MORL benchmark algorithms using aggregate metrics, including median, mean, and interquartile mean (IQM). These results show the superior performance of MORL-FB across all metrics. Recall that MORL-FB leverages PG-Explore to address the fundamental exploration issue of vanilla FB, which suffers from sample inefficiency in MORL. Remarkably, the per-task results in view at source ↗

**Figure 5.** Figure 5: Empirical z distribution under t-SNE for Humanoid2d with MORL-FB (preferenceguided sampling, blue) and original FB (standard normal, red): The multi-modal distribution observed with MORL-FB suggests a more diverse set of latent representations compared to unimodal nature of original FB. [1/d, · · · , 1/d]. The testing setup is exactly the same as that for view at source ↗

**Figure 6.** Figure 6: Evaluation of MORL-FB and its ablated versions on the Ant3d task. The results highlight the importance of PG-Explore and auxiliary losses, as removing these components leads to performance degradation view at source ↗

**Figure 8.** Figure 8: Empirical z distribution under MORL-FB with preference-guided sampling versus Original FB with simple normal distributions on Walker2d view at source ↗

**Figure 9.** Figure 9: Empirical z distribution under MORL-FB with preference-guided sampling versus Original FB with simple normal distributions on Hopper3d. To shows the multi-modality of MORL-FB, we visualized the positions of latent variables z inferred from different preferences on the t-SNE plot in view at source ↗

**Figure 10.** Figure 10: Empirical z distribution under MORL-FB with preference-guided sampling versus Original FB with simple normal distributions on Ant3d view at source ↗

**Figure 11.** Figure 11: Empirical z distribution under MORL-FB with preference-guided sampling (blue) versus view at source ↗

**Figure 12.** Figure 12: Evaluation of MORL-FB and its ablated versions across different environments. The view at source ↗

**Figure 13.** Figure 13: shows the performance of all the methods in UT, HV, and ED for discrete control tasks. Regarding ED, for each baseline algorithm ALG, we report ED(ALG, MORL-FB) to show the pairwise comparison. We can observate that MORL-FB consistently achieves competitive or superior performance across all three metrics on the discrete control tasks Deep Sea Treasure and Fruit Tree Navigation view at source ↗

**Figure 14.** Figure 14: Evaluation of MORL-FB with different reward function representations. This figure presents the performance of MORL-FB when reward functions depend on states only (i.e., R(s)) versus state-action pairs (i.e., R(s, a)). D.5 PERFORMANCE COMPARISON OF MORL-FB UNDER STOCHASTIC REWARDS As vanilla FB naturally handles stochastic rewards, MORL-FB inherits this capability. To further demonstrate this, we evaluated… view at source ↗

**Figure 15.** Figure 15: Evaluation of MORL-FB under stochastic reward. This figure assesses the performance of MORL-FB in environments featuring stochastic reward functions. 30 view at source ↗

**Figure 16.** Figure 16: Performance of MORL-FB on continuous control tasks. We evaluate MORL-FB (1.5M training steps) against several benchmark MORL algorithms (3M training steps) on diverse continuous control tasks from MO-Gymnasium. Utilizing key metrics, these results demonstrate that MORL-FB outperforms baselines, achieving superior HV and UT across most tasks despite significantly fewer training steps view at source ↗

**Figure 17.** Figure 17: Learning curves for MORL-FB and benchmark algorithms on Ant3d. This figure presents the learning curves in terms of Hypervolume (HV) for MORL-FB and several benchmark MORL algorithms evaluated on Ant3d view at source ↗

**Figure 19.** Figure 19: Return vectors (Moving Speed vs. Energy Cost) achieved at the initial, intermediate, view at source ↗

**Figure 20.** Figure 20: Return vectors (Moving Speed vs. Energy Cost) achieved under 21 different preference view at source ↗

**Figure 21.** Figure 21: Probability of Improvement (POI) of MORL-FB against benchmark algorithms. This figure illustrates the POI of MORL-FB relative to various benchmark MORL algorithms. 0.4 0.6 0.8 1.0 PD-MORL Q-Pensieve MORL-FB (Ours) Median 0.4 0.6 0.8 IQM 0.4 0.6 0.8 1.0 Mean Normalized Weighted Reward view at source ↗

**Figure 22.** Figure 22: Medium, IQM, and Mean performance of MORL-FB and benchmarks trained with small preference sets. This figure displays the Median, Interquartile Mean (IQM), and Mean performance for MORL-FB and other benchmark algorithms, trained with only a small set of preference vectors. 0.5 0.6 0.7 0.8 0.9 1.0 P(X < Y) PD-MORL Q-Pensieve Algorithm X MORL-FB (Ours) MORL-FB (Ours) Algorithm Y view at source ↗

**Figure 23.** Figure 23: Probability of Improvement (POI) of MORL-FB under constrained preference training. This figure illustrates the POI of MORL-FB relative to other benchmark algorithms, all trained with specific constraint sets of preference vectors. 37 view at source ↗

read the original abstract

Many sequential decision-making tasks involve optimizing multiple conflicting objectives, requiring policies that adapt to different user preferences. In multi-objective reinforcement learning (MORL), one widely studied approach} addresses this by training a single policy network conditioned on preference-weighted rewards. In this paper, we explore a novel algorithmic perspective: leveraging reward-free reinforcement learning (RFRL) for MORL. While RFRL has historically been studied independently of MORL, it learns optimal policies for any possible reward function, making it a natural fit for MORL's challenge of handling unknown user preferences. We propose using the RFRL's training objective as an auxiliary task to enhance MORL, enabling more effective knowledge sharing beyond the multi-objective reward function given at training time. To this end, we adapt a state-of-the-art RFRL algorithm to the MORL setting and introduce a preference-guided exploration strategy that focuses learning on relevant parts of the environment. Through extensive experiments and ablation studies, we demonstrate that our approach significantly outperforms the state-of-the-art MORL methods across diverse MO-Gymnasium tasks, achieving superior performance and data efficiency. This work provides the first systematic adaptation of RFRL to MORL, demonstrating its potential as a scalable and empirically effective solution to multi-objective policy learning.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper adapts reward-free RL as an auxiliary objective for preference-conditioned MORL plus a new exploration heuristic, and reports gains on MO-Gym tasks, but the combination risks unaddressed gradient conflicts and the empirical support is thin on controls.

read the letter

The main thing to know is that this work treats a reward-free RL objective as an auxiliary loss inside a preference-conditioned MORL policy and adds preference-guided exploration to focus sampling. It claims this yields better performance and data efficiency than prior MORL methods on MO-Gymnasium environments. The framing is new in a systematic way: RFRL already produces behavior that is useful for any reward, so repurposing its training signal to help share knowledge across preferences is a reasonable move rather than a routine extension. The preference-guided exploration is also a concrete, if incremental, addition that tries to avoid wasting samples on irrelevant regions. The paper does a service by running the idea across several tasks and including ablations, which at least lets readers see where the gains appear to come from. That said, the central empirical claim rests on comparisons whose baselines, statistical tests, and variance controls are not laid out clearly enough to judge robustness. More importantly, the RFRL auxiliary term is reward-agnostic by design while the main policy is explicitly conditioned on preference vectors; nothing in the description shows how the two losses are balanced or projected to prevent one from diluting or opposing the other. If the gradients pull in different directions on the shared network, the reported improvements could shrink or become unstable once the weighting is varied. This is the kind of paper that would interest people already working on auxiliary tasks or multi-objective RL who want a practical lever for data efficiency. It is not yet tight enough on the interaction between the objectives or on the experimental details to stand as a finished result, but the idea is coherent and the direction is worth checking. I would send it to peer review so the authors can supply the missing controls and any analysis of the combined objective.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes adapting a state-of-the-art reward-free RL (RFRL) algorithm as an auxiliary training objective for multi-objective RL (MORL), combined with a preference-guided exploration strategy, to improve knowledge sharing across user preferences beyond the given multi-objective reward function. It claims this yields the first systematic RFRL-to-MORL adaptation and significantly outperforms existing MORL methods in performance and data efficiency across diverse MO-Gymnasium tasks.

Significance. If the empirical gains hold under rigorous controls, the work could establish RFRL objectives as a practical auxiliary mechanism for preference-conditioned policies, offering improved data efficiency and generalization in MORL without requiring explicit reward function knowledge at test time.

major comments (2)

[Methods] Methods section: No derivation or stability analysis is provided for combining the RFRL auxiliary objective (which is reward-agnostic and targets coverage or worst-case behavior) with the preference-vector-conditioned MORL policy loss; this leaves open the risk of gradient conflicts or bias toward frequently sampled preferences, as noted in the skeptic concern.
[Experiments] Experiments section: The central claim of outperforming SOTA MORL methods lacks explicit reporting of baseline implementations, number of random seeds, statistical significance tests (e.g., t-tests or confidence intervals), and complete ablation results on the auxiliary objective and exploration strategy, making it impossible to assess whether the reported gains are robust or attributable to the proposed adaptation.

minor comments (1)

[Abstract] Abstract: The phrase 'extensive experiments and ablation studies' is used without naming the specific MO-Gymnasium environments or performance metrics, which reduces clarity for readers scanning the contribution.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments. We address each major point below and indicate the revisions we will incorporate.

read point-by-point responses

Referee: [Methods] Methods section: No derivation or stability analysis is provided for combining the RFRL auxiliary objective (which is reward-agnostic and targets coverage or worst-case behavior) with the preference-vector-conditioned MORL policy loss; this leaves open the risk of gradient conflicts or bias toward frequently sampled preferences, as noted in the skeptic concern.

Authors: We agree that the manuscript does not contain a formal derivation or stability analysis of the combined loss. The approach is presented as an empirical adaptation, motivated by the fact that RFRL objectives encourage state-action coverage that aids generalization across preferences in MORL. In practice, we observed no training instability or obvious bias in the reported runs. To address the concern, we will add a short discussion subsection explaining the objective combination, the use of a fixed weighting hyperparameter to balance the terms, and practical steps (gradient clipping, separate learning rates) that mitigate potential conflicts. This provides a practical treatment without new theoretical claims. revision: partial
Referee: [Experiments] Experiments section: The central claim of outperforming SOTA MORL methods lacks explicit reporting of baseline implementations, number of random seeds, statistical significance tests (e.g., t-tests or confidence intervals), and complete ablation results on the auxiliary objective and exploration strategy, making it impossible to assess whether the reported gains are robust or attributable to the proposed adaptation.

Authors: The manuscript already contains ablation studies isolating the auxiliary objective and exploration strategy (Section 4.3 and Appendix B) and reports performance with means and standard deviations. However, we accept that explicit details on seeds, statistical tests, and baseline code references could be clearer. In the revision we will add a dedicated 'Experimental Setup' paragraph stating the number of random seeds used, the statistical tests performed (including p-values), confidence intervals, and direct links or descriptions of baseline implementations. This will make reproducibility and attribution fully transparent while leaving the empirical results unchanged. revision: yes

Circularity Check

0 steps flagged

No significant circularity: algorithmic adaptation plus empirical validation

full rationale

The paper proposes adapting an existing RFRL algorithm as an auxiliary objective for preference-conditioned MORL policies, augmented by a preference-guided exploration strategy, then validates the combined approach via experiments on MO-Gymnasium benchmarks. No load-bearing derivation, first-principles result, or prediction is presented that reduces by the paper's own equations to a fitted parameter, self-definition, or self-citation chain. The central claims rest on the empirical outperformance rather than any tautological equivalence between inputs and outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard reinforcement-learning assumptions plus the empirical effectiveness of the RFRL-to-MORL adaptation; no new entities or free parameters are explicitly introduced in the abstract.

axioms (1)

domain assumption Standard RL assumptions (Markov decision process, bounded rewards, existence of optimal policies) hold in the MO-Gymnasium environments.
Implicit background for all RL algorithms discussed.

pith-pipeline@v0.9.0 · 5529 in / 1247 out tokens · 26701 ms · 2026-05-08T03:59:55.589261+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

25 extracted references · 7 canonical work pages · 1 internal anchor

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PD-MORL: Preference-driven multi-Objective reinforcement learning algorithm

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Zero-shot whole-body humanoid control via behav- ioral foundation models

13 Published as a conference paper at ICLR 2026 Andrea Tirinzoni, Ahmed Touati, Jesse Farebrother, Mateusz Guzek, Anssi Kanervisto, Yingchen Xu, Alessandro Lazaric, and Matteo Pirotta. Zero-shot whole-body humanoid control via behav- ioral foundation models. InInternational Conference on Learning Representations,

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Finite-time convergence and sample complexity of actor-critic multi-objective reinforcement learning

14 Published as a conference paper at ICLR 2026 Tianchen Zhou, FNU Hairi, Haibo Yang, Jia Liu, Tian Tong, Fan Yang, Michinari Momma, and Yan Gao. Finite-time convergence and sample complexity of actor-critic multi-objective reinforcement learning. InInternational Conference on Machine Learning,

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16 A.2 Forward-Backward (FB) Representations

15 Published as a conference paper at ICLR 2026 APPENDICES A Additional Background: Successor Measure and Forward-Backward Representations 16 A.1 Successor Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 A.2 Forward-Backward (FB) Representations . . . . . . . . . . . . . . . . . . . . . . 17 B Detailed Pseudo Code of MORL-FB...

2026
[12]

what happens next

asz← √dz z ∥z∥2 . This normalization step, motivated by the prior work (Touati et al., 2023), has been observed to improve performance. As shown in Algorithm 2, the training of MORL-FB involves the following loss functions: Measure Loss.The Measure loss,L M(θ, ω;z λ), is central to learning a task-agnostic representation of environment dynamics,F θ(st, at...

2023
[13]

Similar to Humanoid2d, the healthy reward parameter is set to 1.0 to ensure meaningful evaluation

This environment has five objectives: maximizing moving speed along the x-axis, max- imizing moving speed along the y-axis, maximizing angular velocity on the left elbow, maximizing angular velocity on the right elbow, and minimizing energy cost. Similar to Humanoid2d, the healthy reward parameter is set to 1.0 to ensure meaningful evaluation. Classic Con...

2011
[14]

Table 1 and Table 3 list the detailed hyperparameters used in our ex- periments

and CAPQL (Lu et al., 2023). Table 1 and Table 3 list the detailed hyperparameters used in our ex- periments. For PGMORL, the hyperparameters reflect its evolutionary population-based design. The parameterndefines the number of parallel reinforcement learning tasks in each generation. Each task includesm w warm-up iterations andm t evolutionary iterations...

2023
[15]

Table 1: Hyperparameters of PGMORL. Environmentsn m w mt Pnum KP size α HalfCheetah2d6 80 20 100 2 7−1 Walker2d6 80 20 100 2 7−1 Hopper3d15 200 40 210 2 7−10 6 Ant3d15 200 40 210 2 7−10 6 Humanoid2d6 200 40 100 2 7−1 Humanoid5d35 200 40 550 2 7−10 6 20 Published as a conference paper at ICLR 2026 Table 2: PPO hyperparameters used in PGMORL. Parameter Valu...

2026
[16]

Point) for each environment

Reference Points for HV Evaluation.We compute the HV indicator using predefined reference points (Ref. Point) for each environment. These reference points serve as baselines to measure the 23 Published as a conference paper at ICLR 2026 Table 12: Hyperparameter configuration for MORL-FB experiments. Parameter Value Total number of environment steps3×10 6 ...

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[17]

Ant3d (0, 0, -8000) Humanoid2d (0, -8000) Humanoid5d (0, 0, 0, 0, -8000) C.3 COMPUTERESOURCES All models were trained on a workstation featuring a single NVIDIA RTX 4090 GPU, an Intel Core i7-13700K CPU, and 64 GB of system memory. 24 Published as a conference paper at ICLR 2026 D ADDITIONALEXPERIMENTALRESULTS D.1 VISUALIZATION OFzDISTRIBUTION INDIFFERENT...

2026
[18]

Original

This demonstrates that MORL-FB ef- fectively encodes different preferences into separate regions of the latent space, leading to more diverse policies. To further illustrate this, we provide a demo of the policies learned by MORL-FB and vanilla FB in this link:https://imgur.com/a/ehx1v7q, where the z’s are selected from different positions on the t-SNE pl...

2026
[19]

auxiliary

This shows that the auxiliary loss of FB cannot be directly applied and needs to be adapted properly in the context of MORL. Note that we use the term “auxiliary” since the original FB is directly built on the measure loss and hence the Q loss is auxiliary for learning FB representation, rather than being unimportant for MORL. Table 16: Ablation study of ...

2026
[20]

Since some MO MuJoCo rewards depend on both states and actions, we compare MORL-FB and the extended one

and state-action-based rewards (Touati & Ollivier, 2021), MORL-FB can also be extended to state-action-based rewards by replacingB(s)withB(s, a). Since some MO MuJoCo rewards depend on both states and actions, we compare MORL-FB and the extended one. As shown in the Figure 14, the state-action-based variant yields slight performance improvements on severa...

2021
[21]

Figure 15:Evaluation of MORL-FB under stochastic reward.This figure assesses the perfor- mance of MORL-FB in environments featuring stochastic reward functions. 30 Published as a conference paper at ICLR 2026 D.6 PERFORMANCECOMPARISON OFMORL-FB WITHNONLINEARSCALARIZATION While we focus on linear scalarization in this paper, MORL-FB can be readily extended...

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[22]

D.9 RFRLAS A SOURCE OF AUXILIARY TASKS During training, thezvectors computed for each preferenceλare diverse, covering both CCS and non-CCS policies

MORL-FB consistently outperforms FB across all configurations in terms of utility and hypervolume. D.9 RFRLAS A SOURCE OF AUXILIARY TASKS During training, thezvectors computed for each preferenceλare diverse, covering both CCS and non-CCS policies. Learning from non-CCS policies serves as auxiliary tasks. From Figure 19, we find that the return vectors ac...

2026
[23]

34 Published as a conference paper at ICLR 2026 Table 22: Wall-clock time comparison (100K steps)

The results in Tables 23 to 26 correspond to the visualizations shown in Figure 2, Figure 4, Figure 12 and Figure 13, respectively. 34 Published as a conference paper at ICLR 2026 Table 22: Wall-clock time comparison (100K steps). Algorithm Wall-Clock Time (seconds) PD-MORL 1166 CAPQL 3369 MORL/D 793 SFOLS 550 Q-Pensieve 12960 PGMORL 4237 PCN 4445 GPI-LS ...

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2.38±0.30 -1.43±0.148.13±0.01 HV(×10 7)1.78±0.000.96±0.00 1.75±0.02 35 Published as a conference paper at ICLR 2026 Table 26: Comparative performance of MORL-FB and various benchmark algorithms across continuous control tasks in MuJoCo. Environments Metrics PD-MORL Q-Pensieve CAPQL PGMORL MORL/D PCN SFOLS GPI-LS GPI-PD FB MORL-FB (w/o interpolator) (Ours)...

2026
[25]

The results demonstrate that MORL-FB consistently achieves superior performance compared to baselines

POI quantifies the likelihood that one algorithm will outperform another. The results demonstrate that MORL-FB consistently achieves superior performance compared to baselines. Additionally, we assessed the performance of training with constraint preferences using the method from Agarwal et al. (2021), presented in Figures 22 and

2021