Behavioral Diversity in RL

Reinforcement Learning with Verifiable Rewards (RLVR) improves the reasoning capabilities of large language models, but often reduces the diversity of their reasoning behaviors. We study this phenomenon from the perspective of finite-sample learning dynamics and show that limited on-policy rollouts can progressively suppress semantically distinct but equally rewarded reasoning modes. Once a mode becomes sufficiently under-sampled, standard on-policy RLVR rarely recovers it. Motivated by this observation, we propose TAR, a Targeted Adaptive Replay framework that preserves diverse correct reasoning behaviors already present in the base policy. TAR constructs a compact memory bank of diverse base-model solutions and selectively replays them through an adaptive mechanism that activates only when stored behaviors are being suppressed during RLVR. Across six mathematical reasoning benchmarks and two Qwen2.5 model scales, TAR consistently achieves a better balance between reasoning performance and diversity preservation than existing diversity-preserving post-training methods, while substantially reducing the forgetting of correct base-model solutions. Code is available at https://github.com/wenzhilics/tar.

Reinforcement learning has become a common post-training technique to improve the accuracy of LLMs on verifiable tasks. However, such training can narrow the set of solutions the model can produce. Several approaches have attempted to address this behavior-sharpening effect, but they often optimize metrics that do not reflect the diversity of correct solutions. Ideally, we want a model that can produce multiple good solutions, not only a single reliable one. We propose EliteReplay, a post-training recipe that pairs GRPO with an "elite" archive built by quality-diversity search. Before training, we use the frozen base model to collect solutions that span distinct approaches; during training, GRPO is combined with a replay loss on this archive. The result is a post-trained model that improves accuracy while preserving more of the base model's solution diversity. On multiple text-to-SQL tasks, EliteReplay achieves a higher pass@128 than all baselines, producing up to 77% more distinct correct strategies than the strongest baselines. It preserves most of the base model's correct strategies, outperforming existing methods in strategy retention. This diversity translates into practical benefits on ambiguous questions, where EliteReplay covers both interpretations nearly twice as often as the strongest baseline on AmbiQT.

In cooperative Multi-Agent Reinforcement Learning (MARL), agents must learn to coordinate their actions to achieve shared objectives. A key indicator of effective coordination is behavioral diversity, i.e., the agents' potential to enact distinct yet complementary control policies given the same set of observations. Although behavioral diversity can enable role specialization and richer joint behaviors, its appropriate level is highly context- and task-dependent and often costly to tune. We propose Adaptive Diversity Control (ADiCo), a two-timescale framework that adapts behavioral diversity online during training. On a fast timescale, Diversity Control (DiCo) regulates system diversity toward a target value. On a slower timescale, an Extremum Seeking Controller (ESC) adjusts this target using only mean episodic returns, without requiring an explicit model or analytical gradient of the diversity-performance landscape. We evaluate ADiCo on six configurations across two cooperative MARL tasks, where it maintains task-appropriate diversity levels: low diversity when homogeneous policies are beneficial and higher diversity when heterogeneous policies are required. Through this adaptation, ADiCo matches or exceeds the mean performance of DiCo (best grid-searched diversity target) and Unconstrained DiCo (diversity allowed to emerge without target regulation). These results demonstrate that incorporating classical feedback control into MARL training enables effective coordination by providing a systematic alternative to task-specific manual selection of the diversity target.

Behavioral Foundation Models (BFMs) are an emerging paradigm in reinforcement learning, playing a role analogous to large language models in natural language processing: they have shown remarkable versatility, enabling zero-shot performance, fast imitation, and online adaptation, all by exploiting the structure of a latent space. In this work, we investigate whether the latent behavioral space induced by BFMs can serve as an effective search space to discover large repertoires of behaviorally diverse and high-performing policies through Quality-Diversity (QD) methods. While QD methods generally search directly in high-dimensional policy parameter space, in this paper, we present BFM-QD, a framework that performs QD search in the compact latent space of a BFM. We further show that the BFM-QD framework provides a closed-form, gradient-free policy improvement operator that approximates a policy gradient update, but requires no critic training and no backpropagation. Across continuous-control benchmarks spanning dense locomotion, sparse navigation, and contact-rich manipulation, BFM-QD consistently outperforms parameter-space baselines, with particularly stark gains in sparse and deceptive settings, where all tested parameter-space QD methods collapse to near-zero performance. These results show the effectiveness of the BFM-QD framework, benefiting from the synergy between dimensionality reduction of the search space and offline pretraining from diverse behavioral data. This positions BFMs as a general-purpose backbone for QD optimization, extending their utility beyond zero-shot task solving to the discovery of diverse behavioral repertoires.

Reinforcement learning (RL) is primarily known as a computational method for optimizing control tasks, but it is increasingly used to explain biological behavior. While RL successfully captures key aspects of biology, a major gap remains: between-agent behavioral variability. Consistent individual differences naturally permeate biological populations, yet RL models typically present only the single best individual or the population average. Addressing this gap requires moving beyond current practices to generate behavioral diversity using biologically plausible mechanisms. Here, we examine approaches from various subfields of RL and outline potential paths forward to close the gap between biology and simulation.

Real-world decision-making often requires optimizing multiple competing objectives simultaneously. In reinforcement learning (RL), this is typically addressed by combining reward signals into a single scalar objective via a scalarization function, which can be fragile: small changes in the weights can induce drastically different policies. Multi-objective reinforcement learning (MORL) instead produces sets of policies that explicitly represent trade-offs between objectives. However, these policies are typically presented to the decision maker only through their value vectors, which can obscure substantial behavioral variation: policies that induce distinct trajectories may appear indistinguishable when evaluated solely by expected returns. We propose an exploratory diagnostic workflow that automatically highlights behavioral variation along the Pareto front that objective values alone do not reveal, providing both quantitative and visual tools to support policy inspection. We validate our approach on simple grid examples and scale it to continuous control benchmarks, demonstrating that it remains effective as problem complexity increases.

Quality-diversity reinforcement learning (QD-RL) aims to construct policy repertoires that contain both high-performing and behaviorally diverse policies. Existing QD-RL methods mainly diversify policy instances after rollout evaluation or use learned value information to improve policy quality and behavior targeting, while the learning branches that generate candidate policies remain less explored. This paper proposes SV-QD-RL, a structure-value coupled framework that represents each candidate as a structure-conditioned actor-critic branch. Each branch contains an actor, a structural mask, a branch-specific critic, a replay state, and evaluation attributes including behavior, return, sparsity, and value profile. The structural mask defines the actor subspace in which the branch learns, while the branch-specific critic and replay state shape its value-learning trajectory. A branch-aware QD archive then evaluates and retains branches according to behavioral quality, structural footprint, and value-profile information. Experiments on MuJoCo continuous-control tasks show that SV-QD-RL constructs policy repertoires with strong archive quality and behaviorally useful diversity. Ablation and diagnostic analyses further indicate that structural conditioning, critic differentiation, and memory-consistent refinement make complementary contributions to behavioral specialization. Schedule-aware repertoire evaluation shows that the learned archive provides selectable policy alternatives under changing behavior-level requirements. These results suggest that coupling actor structure with branch-specific value learning is an effective mechanism for generating diverse QD-RL policy repertoires.

Classical reinforcement learning (RL) typically seeks a deterministic policy that maximizes the expected sum of a scalar reward. Yet, modern applications such as language model fine-tuning or scientific discovery demand diversity. Existing remedies such as entropy regularization or diversity bonuses often require fragile trade-offs that sacrifice performance for stochasticity or rely on heuristic metrics that can misalign policy rankings. We argue that diversity is more naturally understood as the rational response to uncertainty in the reward. When the reward function is not perfectly known--as is the case with ambiguous preferences or imperfect reward models--committing to a single action can be sub-optimal. Building on this, we propose a fundamental reformulation of the RL objective by replacing the scalar reward with a distribution over reward functions, and applying a non-linear objective over sets of actions. The result is a framework in which calibrated behavioural diversity emerges naturally, remains controllable through the reward function distribution, and is obtained without sacrificing expected reward. Focusing on the contextual bandit setting as commonly used in large language model (LLM) post-training, we derive a principled gradient estimator for this objective and prove that our formulation naturally generalizes both vanilla policy gradient and more recently developed action-set approaches. We provide didactic experiments which complement our theoretical results, and our large-scale empirical results in LLM reasoning further demonstrate that this framework offers a robust and theoretically grounded alternative for complex RL tasks where the traditional formulation of the problem fails to induce the desired breadth of agent behaviour.

Reinforcement learning with verifiable rewards (RLVR) trains reasoning models without labeled trajectories, using groups of verifier-scored rollouts to explore alternative reasoning paths. Limited rollout diversity is a central bottleneck, typically addressed through adjustments to temperature, prefixes, or rollout selection. We identify the first token of the response as a structurally distinct target for diversification, largely overlooked in prior work. We find that the first-token distribution is sharply concentrated and only weakly related to downstream correctness, as lower-probability candidates can yield similarly accurate responses. Diversifying the first token can therefore broaden the reasoning paths explored within each rollout group with little loss in response quality. Motivated by this observation, we introduce REFT (Rollout Exploration with First-Token Diversification), a lightweight modification to RLVR. REFT samples first tokens uniformly from the policy's top-$N$ candidates and allocates rollouts evenly across the sampled tokens, leaving the rest of the pipeline unchanged. We evaluate REFT on eight models spanning multiple architectures and sizes (0.5B-14B), with mathematical reasoning and code-generation tasks under GRPO and DAPO. Across these settings, REFT consistently improves Pass@1, Pass@8, and Pass@64. It also outperforms competing diversification methods at every evaluated budget, incurring the lowest rollout cost.

On-policy reinforcement learning methods like GRPO suffer from mode collapse: they exhibit reduced solution diversity, concentrating probability mass on a single solution once discovered and ceasing exploration of alternative strategies. We show this stems from reverse KL minimization's mode-seeking behavior, which reinforces the first high-reward trajectory found rather than maintaining a distribution over multiple diverse solutions. We propose DMPO (Distribution-Matching Policy Optimization), which prevents mode collapse through principled approximation of forward KL minimization. DMPO constructs a group level target distribution over sampled trajectories proportional to their rewards, then aligns the policy distribution to this target. This provides mode-covering behavior without requiring sampling from the intractable global target distribution, enabling sustained exploration throughout training. We validate DMPO on NP-hard combinatorial optimization, where exponentially many feasible solutions exist but only a few approach optimality, an ideal testbed for evaluating exploration. DMPO achieves 43.9% Quality Ratio on text-based NP-Bench (vs. GRPO's 40.1%) and 43.1% on vision-based NP-Bench (vs. 38.4%), demonstrating 9% and 12% relative improvements respectively. These gains generalize to mathematical reasoning (+2.0%) and out-of-domain tasks (+2.3%), showing that diversity-preserving training enhances general reasoning capabilities across modalities. Our work establishes distribution matching as a practical, principled approach to preventing mode collapse in on-policy RL, with consistent quality improvements demonstrating sustained exploration across diverse reasoning tasks.

Effective multi-agent cooperation requires agents to adopt diverse behaviors as task conditions evolve-and to do so at the right moment. Yet, current Multi-Agent Reinforcement Learning (MARL) frameworks that facilitate this diversity are still limited by the fact that they bind fixed behaviors to fixed agent identities. Consequently, they are ill-equipped for tasks where agents need to take on different roles at very specific moments in time. We argue that, to define these behavioral transitions, the missing ingredient is $\textbf{events}$. Events are changes in the state of the system that induce qualitative changes in the task. Based on this view, we introduce a framework that decouples agent identity from behavior, capturing a continuous manifold from which agents instantiate their behaviors in response to events. This framework is based on two elements. First, to build an expressive behavior manifold, we introduce Neural Manifold Diversity (NMD), a formal distance metric that remains well-defined when behaviors are transient and agent-agnostic. Second, we use an event-based hypernetwork that generates Low-Rank Adaptation (LoRA) modules over a shared team policy, enabling on-the-fly agent-policy reconfiguration in response to events. We prove that this construction ensures that diversity does not interfere with reward maximization by design. Empirical results demonstrate that our framework outperforms established baselines across benchmarks while exhibiting zero-shot generalization, and being the only method that solves tasks requiring sequential behavior reassignment.

We address the problem of fine-tuning pre-trained generative policies with reinforcement learning (RL) while preserving the multimodality of their action distributions. Existing methods for RL fine-tuning of generative policies (e.g., diffusion policies) improve task performance but often collapse diverse behaviors into a single reward-maximizing mode. To mitigate this issue, we propose an unsupervised mode discovery framework that uncovers latent behavioral modes within generative policies. The discovered modes enable the use of mutual information as an intrinsic reward, regularizing RL fine-tuning to enhance task success while maintaining behavioral diversity. Experiments on robotic manipulation tasks demonstrate that our method consistently outperforms conventional fine-tuning approaches, achieving higher success rates and preserving richer multimodal action distributions.

System Neural Diversity (SND) measures behavioral heterogeneity in multi-agent reinforcement learning by averaging pairwise distances over all $\binom{n}{2}$ agent pairs, making each call quadratic in team size. We introduce Graph-SND, which replaces this complete-graph average with a weighted average over the edges of an arbitrary graph $G$. Three regimes follow: $G=K_n$ recovers SND exactly; a fixed sparse $G$ defines a localized diversity measure at $O(|E|)$ cost; and random edge samples yield an unbiased Horvitz-Thompson estimator and a normalized sample mean with $O(1/\sqrt{m})$ concentration in the sampled edge count $m$. For fixed sparse graphs we prove forwarding-index distortion bounds for expanders and a spectral refinement under low-rank distance structure; for random $d$-regular graphs we prove an unconditional probabilistic $\widetilde{\mathcal{O}}(D_{\max}/\sqrt{n})$ bound. On VMAS we verify recovery, unbiasedness, concentration, and wall-clock scaling, with a PettingZoo TVD panel checking non-Gaussian transfer. In a 500-iteration $n=100$ PPO run, Bernoulli-$0.1$ Graph-SND tracks full SND while reducing per-call metric time by about $10\times$, and frozen-policy GPU timing up to $n=500$ follows the predicted $\binom{n}{2}/|E|$ speedup. Random $d$-regular expanders empirically achieve $\mathrm{SND}_{G}^{\mathrm{u}}/\mathrm{SND} \in [0.9987, 1.0013]$ at $Θ(n \log n)$ edges. In DiCo diversity control at $n=50$, Bernoulli-$0.1$ Graph-SND preserves set-point tracking with paired reward differences indistinguishable from zero across nine matched cells while cutting per-call metric cost by ${\sim}9.5\times$. Together, these results show that the SND aggregation bottleneck can be removed without changing the metric's semantics, yielding a drop-in sparse alternative that scales beyond complete-graph SND and supports both passive measurement and closed-loop diversity control.

Reinforcement learning with verifiable rewards (RLVR) has become a standard approach for improving reasoning in language models, yet models trained with RLVR often suffer from diversity collapse: while single-sample accuracy improves, multi-sample coverage degrades, sometimes falling below the base model. We provide a structural account of this phenomenon grounded in the properties of binary rewards. Binary rewards create a fundamental degeneracy for policy gradient methods: the set of distributions maximizing expected reward is infinite, with no distinguished element. KL-control resolves this degeneracy by selecting, in the limit $β\to 0$, the filtered model $p_*:=a(\cdot\mid\mathcal{Y}_1)$ -- the base model conditioned on validity -- which is the unique fully valid distribution closest to the base model in KL divergence. This selection operates through a nontrivial asymmetry: the tilted distribution $p_{[β]}\propto a(y)\,e^{v(y)/β}$ converges to $p_*$ in forward KL as $β\to 0$, yet $p_*$ cannot serve as a direct optimization target because $\mathrm{KL}(q\,\|\,p_*)$ is infinite for any full-support policy $q$. We develop explicit formulas relating the hyperparameter $β$ to the more interpretable target validity rate $μ$. Under model misspecification -- the typical practical regime -- the pressure to decrease $β$ drives the optimizer toward highly concentrated distributions over a small number of valid outputs, collapsing toward ever fewer as $β$ decreases, rather than toward the filtered model. We illustrate this mechanism on a toy autoregressive experiment and discuss how alternative divergences that target $p_*$ directly -- as pursued empirically by \citet{kruszewski_whatever_2026} -- avoid this failure mode by rewarding coverage of $p_*$'s support rather than concentration on high-validity outputs.

Reinforcement Learning with Verifiable Rewards (RLVR) has achieved substantial gains in single-attempt accuracy (Pass@1) on reasoning tasks, yet often suffers from reduced multi-sample coverage (Pass@K), indicating diversity collapse. We identify a structural cause for this degradation: common RLVR objectives, such as GRPO, are indifferent to how probability mass is distributed among correct solutions. Combined with stochastic training dynamics, this indifference induces a self-reinforcing collapse, in which probability mass concentrates on a narrow subset of correct outputs while alternative valid solutions are suppressed. We formalize this collapse mechanism and further characterize the optimal policy structure under two complementary criteria: robustness and entropy-regularized optimality, which identify the Uniform-Correct Policy as uniquely optimal. Motivated by this analysis, we propose Uniform-Correct Policy Optimization (UCPO), a modification to GRPO that adds a conditional uniformity penalty on the policy's distribution over correct solutions. The penalty redistributes gradient signal toward underrepresented correct responses, encouraging uniform allocation of probability mass within the correct set. Across three models (1.5B-7B parameters) and five mathematical reasoning benchmarks, UCPO improves Pass@K and diversity while maintaining competitive Pass@1, achieving up to +10% absolute improvement on AIME24 at Pass@64 and up to 45% higher equation-level diversity within the correct set. The code is available at https://github.com/AnamikaLochab/UCPO.

Quality-Diversity (QD) algorithms excel at discovering diverse repertoires of skills, but are hindered by poor sample efficiency and often require tens of millions of environment steps to solve complex locomotion tasks. Recent advances in Reinforcement Learning (RL) have shown that high Update-to-Data (UTD) ratios accelerate Actor-Critic learning. While effective, standard high-UTD algorithms typically utilise target networks to stabilise training. This requirement introduces a significant computational bottleneck, rendering them impractical for resource-intensive Quality-Diversity (QD) tasks where sample efficiency and rapid population adaptation are critical. In this paper, we introduce QDHUAC, a sample-efficient, target-free and distributional QD-RL algorithm that provides dense and low-variance gradient signals, which enables high-UTD training for Dominated Novelty Search whilst requiring an order of magnitude fewer environment steps. We demonstrate that our method enables stable training at high UTD ratios, achieving competitive coverage and fitness on high-dimensional Brax environments with an order of magnitude fewer samples than baselines. Our results suggest that combining target-free distributional critics with dominance-based selection is a key enabler for the next generation of sample-efficient evolutionary RL algorithms.

Despite the success of reinforcement learning for large language models, a common failure mode is reduced sampling diversity, where the policy repeatedly generates similar erroneous behaviors. Classical entropy regularization encourages randomness under the current policy, but does not explicitly discourage recurrent failure patterns across rollouts. We propose MEDS, a Memory-Enhanced Dynamic reward Shaping framework that incorporates historical behavioral signals into reward design. By storing and leveraging intermediate model representations, we capture features of past rollouts and use density-based clustering to identify frequently recurring error patterns. Rollouts assigned to more prevalent error clusters are penalized more heavily, encouraging broader exploration while reducing repeated mistakes. Across five datasets and three base models, MEDS consistently improves average performance over existing baselines, achieving gains of up to 4.13 pass@1 points and 4.37 pass@128 points. Additional analyses using both LLM-based annotations and quantitative diversity metrics show that MEDS increases behavioral diversity during sampling.

Zero-shot reinforcement learning (RL) algorithms aim to learn a family of policies from a reward-free dataset, and recover optimal policies for any reward function directly at test time. Naturally, the quality of the pretraining dataset determines the performance of the recovered policies across tasks. However, pre-collecting a relevant, diverse dataset without prior knowledge of the downstream tasks of interest remains a challenge. In this work, we study $\textit{online}$ zero-shot RL for quadrupedal control on real robotic systems, building upon the Forward-Backward (FB) algorithm. We observe that undirected exploration yields low-diversity data, leading to poor downstream performance and rendering policies impractical for direct hardware deployment. Therefore, we introduce FB-MEBE, an online zero-shot RL algorithm that combines an unsupervised behavior exploration strategy with a regularization critic. FB-MEBE promotes exploration by maximizing the entropy of the achieved behavior distribution. Additionally, a regularization critic shapes the recovered policies toward more natural and physically plausible behaviors. We empirically demonstrate that FB-MEBE achieves and improved performance compared to other exploration strategies in a range of simulated downstream tasks, and that it renders natural policies that can be seamlessly deployed to hardware without further finetuning. Videos and code available on our website.

While Reinforcement Learning (RL) enhances Large Language Model reasoning, on-policy algorithms like GRPO are sample-inefficient as they discard past rollouts. Existing experience replay methods address this by reusing accurate samples for direct policy updates, but this can incur additional storage costs and concentrate the policy on a narrow set of solutions. We argue that historical data should prioritize sustaining local policy plasticity rather than simply reinforcing accuracy. We define local policy plasticity as a persistent ability to remain backtrackable and switchable with respect to recent successful trajectories: throughout training, the policy maintains non-negligible support on recently reachable alternatives, so it can smoothly reallocate probability mass when needed without being locked into a single dominant path. To this end, we propose Dynamic Jensen-Shannon Replay (DyJR), a simple yet effective regularization framework using a dynamic reference distribution from recent trajectories. DyJR introduces two innovations: (1) A Time-Sensitive Dynamic Buffer that uses FIFO and adaptive sizing to retain only temporally proximal samples, synchronizing with model evolution; and (2) Jensen-Shannon Divergence Regularization, which replaces direct replay policy-gradient updates with a regularization signal that discourages premature over-commitment to a single Rank-1 trajectory. Experiments on mathematical reasoning, Text-to-SQL, and coding benchmarks demonstrate that DyJR improves over GRPO as well as baselines such as RLEP and Ex-GRPO, while maintaining training efficiency comparable to the original GRPO. Furthermore, Rank-k token probability evolution and semantic-mode analyses show reduced concentration and greater retention of alternative continuations. Matched admission-objective comparisons and repeated runs provide additional evidence for the roles of DyJR's components.

Policy gradient algorithms have driven many recent advancements in language model reasoning. An appealing property is their ability to learn from exploration on their own trajectories, a process crucial for fostering diverse and creative solutions. As we show in this paper, many policy gradient algorithms naturally reduce the entropy -- and thus the diversity of explored trajectories -- as part of training, yielding a policy increasingly limited in its ability to explore. In this paper, we argue that entropy should be actively monitored and controlled throughout training. We formally analyze the contributions of leading policy gradient objectives on entropy dynamics, identify empirical factors (such as numerical precision) that significantly impact entropy behavior, and propose explicit mechanisms for entropy control. These include REPO, a family of algorithms that modify the advantage function to regulate entropy, and ADAPO, an adaptive asymmetric clipping approach. Models trained with our entropy-preserving methods maintain diversity throughout training, yielding final policies that are more performant and retain their trainability for sequential learning in new environments.

Proficient game agents with diverse play styles enrich the gaming experience and enhance the replay value of games. However, recent advancements in game AI based on reinforcement learning have predominantly focused on improving proficiency, whereas methods based on evolution algorithms generate agents with diverse play styles but exhibit subpar performance compared to RL methods. To address this gap, this paper proposes Mixed Proximal Policy Optimization (MPPO), a method designed to improve the proficiency of existing suboptimal agents while retaining their distinct styles. MPPO unifies loss objectives for both online and offline samples and introduces an implicit constraint to approximate demonstrator policies by adjusting the empirical distribution of samples. Empirical results across environments of varying scales demonstrate that MPPO achieves proficiency levels comparable to, or even superior to, pure online algorithms while preserving demonstrators' play styles. This work presents an effective approach for generating highly proficient and diverse game agents, ultimately contributing to more engaging gameplay experiences.

Temporal abstraction allows reinforcement learning agents to represent knowledge and develop strategies over different temporal scales. The option-critic framework has been demonstrated to learn temporally extended actions, represented as options, end-to-end in a model-free setting. However, feasibility of option-critic remains limited due to two major challenges, multiple options adopting very similar behavior, or a shrinking set of task relevant options. These occurrences not only void the need for temporal abstraction, they also affect performance. In this paper, we tackle these problems by learning a diverse set of options. We introduce an information-theoretic intrinsic reward, which augments the task reward, as well as a novel termination objective, in order to encourage behavioral diversity in the option set. We show empirically that our proposed method is capable of learning options end-to-end on several discrete and continuous control tasks, outperforms option-critic by a wide margin. Furthermore, we show that our approach sustainably generates robust, reusable, reliable and interpretable options, in contrast to option-critic.