-- We introduce Multi-CALF, an algorithm that intelligently combines reinforcement learning policies based on their relative value improvements. We prove that our combined policy converges to a specified goal set with known probability and provide precise bounds on maximum deviation and convergence time. Empirical validation on control tasks demonstrates enhanced performance while maintaining stability guarantees. I. INTRODUCTION Reinforcement learning (RL) has demonstrated remarkable effectiveness for solving complex control problems across diverse domains, from robotic manipulation [1], [2], [3], [4] to games [5], [6], [7]. Policy synthesis [12], [13], which combines policies with complementary strengths, has emerged as a promising approach to address these limitations.

Offline reinforcement learning seeks to derive improved policies entirely from historical data but often struggles with over-optimistic value estimates for out-of-distribution (OOD) actions. This issue is typically mitigated via policy constraint or conservative value regularization methods. However, these approaches may impose overly constraints or biased value estimates, potentially limiting performance improvements. To balance exploitation and restriction, we propose an Imagination-Limited Q-learning (ILQ) method, which aims to maintain the optimism that OOD actions deserve within appropriate limits. Specifically, we utilize the dynamics model to imagine OOD action-values, and then clip the imagined values with the maximum behavior values. Such design maintains reasonable evaluation of OOD actions to the furthest extent, while avoiding its over-optimism. Theoretically, we prove the convergence of the proposed ILQ under tabular Markov decision processes. Particularly, we demonstrate that the error bound between estimated values and optimality values of OOD state-actions possesses the same magnitude as that of in-distribution ones, thereby indicating that the bias in value estimates is effectively mitigated. Empirically, our method achieves state-of-the-art performance on a wide range of tasks in the D4RL benchmark.

Object insertion under tight tolerances ($< \hspace{-.02in} 1mm$) is an important but challenging assembly task as even small errors can result in undesirable contacts. Recent efforts focused on Reinforcement Learning (RL), which often depends on careful definition of dense reward functions. This work proposes an effective strategy for such tasks that integrates traditional model-based control with RL to achieve improved insertion accuracy. The policy is trained exclusively in simulation and is zero-shot transferred to the real system. It employs a potential field-based controller to acquire a model-based policy for inserting a plug into a socket given full observability in simulation. This policy is then integrated with residual RL, which is trained in simulation given only a sparse, goal-reaching reward. A curriculum scheme over observation noise and action magnitude is used for training the residual RL policy. Both policy components use as input the SE(3) poses of both the plug and the socket and return the plug's SE(3) pose transform, which is executed by a robotic arm using a controller. The integrated policy is deployed on the real system without further training or fine-tuning, given a visual SE(3) object tracker. The proposed solution and alternatives are evaluated across a variety of objects and conditions in simulation and reality. The proposed approach outperforms recent RL-based methods in this domain and prior efforts with hybrid policies. Ablations highlight the impact of each component of the approach.

The dependency of the actor on the critic in actor-critic (AC) reinforcement learning means that AC can be characterized as a bilevel optimization (BLO) problem, also called a Stackelberg game. This characterization motivates two modifications to vanilla AC algorithms. First, the critic's update should be nested to learn a best response to the actor's policy. Second, the actor should update according to a hypergradient that takes changes in the critic's behavior into account. Computing this hypergradient involves finding an inverse Hessian vector product, a process that can be numerically unstable. We thus propose a new algorithm, Bilevel Policy Optimization with Nyström Hypergradients (BLPO), which uses nesting to account for the nested structure of BLO, and leverages the Nyström method to compute the hypergradient. Theoretically, we prove BLPO converges to (a point that satisfies the necessary conditions for) a local strong Stackelberg equilibrium in polynomial time with high probability, assuming a linear parametrization of the critic's objective. Empirically, we demonstrate that BLPO performs on par with or better than PPO on a variety of discrete and continuous control tasks.

When tackling complex problems, humans naturally break them down into smaller, manageable subtasks and adjust their initial plans based on observations. For instance, if you want to make coffee at a friend's place, you might initially plan to grab coffee beans, go to the coffee machine, and pour them into the machine. Upon noticing that the machine is full, you would skip the initial steps and proceed directly to brewing. In stark contrast, state of the art reinforcement learners, such as Proximal Policy Optimization (PPO), lack such prior knowledge and therefore require significantly more training steps to exhibit comparable adaptive behavior. Thus, a central research question arises: \textit{How can we enable reinforcement learning (RL) agents to have similar ``human priors'', allowing the agent to learn with fewer training interactions?} To address this challenge, we propose differentiable symbolic planner (Dylan), a novel framework that integrates symbolic planning into Reinforcement Learning. Dylan serves as a reward model that dynamically shapes rewards by leveraging human priors, guiding agents through intermediate subtasks, thus enabling more efficient exploration. Beyond reward shaping, Dylan can work as a high level planner that composes primitive policies to generate new behaviors while avoiding common symbolic planner pitfalls such as infinite execution loops. Our experimental evaluations demonstrate that Dylan significantly improves RL agents' performance and facilitates generalization to unseen tasks.

We develop Policy Gradient with Second-Order Momentum (PG-SOM), a lightweight second-order optimisation scheme for reinforcement-learning policies. PG-SOM augments the classical REINFORCE update with two exponentially weighted statistics: a first-order gradient average and a diagonal approximation of the Hessian. By preconditioning the gradient with this curvature estimate, the method adaptively rescales each parameter, yielding faster and more stable ascent of the expected return. We provide a concise derivation, establish that the diagonal Hessian estimator is unbiased and positive-definite under mild regularity assumptions, and prove that the resulting update is a descent direction in expectation. Numerical experiments on standard control benchmarks show up to a 2.1x increase in sample efficiency and a substantial reduction in variance compared to first-order and Fisher-matrix baselines. These results indicate that even coarse second-order information can deliver significant practical gains while incurring only D memory overhead for a D-parameter policy. All code and reproducibility scripts will be made publicly available.

Recent research highlights the potential of multimodal foundation models in tackling complex decision-making challenges. However, their large parameters make real-world deployment resource-intensive and often impractical for constrained systems. Reinforcement learning (RL) shows promise for task-specific agents but suffers from high sample complexity, limiting practical applications. To address these challenges, we introduce LVLM to Policy (LVLM2P), a novel framework that distills knowledge from large vision-language models (LVLM) into more efficient RL agents. Our approach leverages the LVLM as a teacher, providing instructional actions based on trajectories collected by the RL agent, which helps reduce less meaningful exploration in the early stages of learning, thereby significantly accelerating the agent's learning progress. Additionally, by leveraging the LVLM to suggest actions directly from visual observations, we eliminate the need for manual textual descriptors of the environment, enhancing applicability across diverse tasks. Experiments show that LVLM2P significantly enhances the sample efficiency of baseline RL algorithms.

Exploration remains a critical challenge in online reinforcement learning, as an agent must effectively explore unknown environments to achieve high returns. Currently, the main exploration algorithms are primarily count-based methods and curiosity-based methods, with prediction-error methods being a prominent example. In this paper, we propose a novel method called \textbf{R}andom \textbf{D}istribution \textbf{D}istillation (RDD), which samples the output of a target network from a normal distribution. RDD facilitates a more extensive exploration by explicitly treating the difference between the prediction network and the target network as an intrinsic reward. Furthermore, by introducing randomness into the output of the target network for a given state and modeling it as a sample from a normal distribution, intrinsic rewards are bounded by two key components: a pseudo-count term ensuring proper exploration decay and a discrepancy term accounting for predictor convergence. We demonstrate that RDD effectively unifies both count-based and prediction-error approaches. It retains the advantages of prediction-error methods in high-dimensional spaces, while also implementing an intrinsic reward decay mode akin to the pseudo-count method. In the experimental section, RDD is compared with more advanced methods in a series of environments. Both theoretical analysis and experimental results confirm the effectiveness of our approach in improving online exploration for reinforcement learning tasks.

Theory of Mind (ToM), the ability to attribute mental states to others, is fundamental for human social intelligence and a critical capability for advanced Artificial Intelligence. Recent advancements in Large Language Models (LLMs) have shown promising performance on ToM benchmarks, raising the question: Do these benchmarks necessitate explicit human-like reasoning processes, or can models succeed through alternative strategies? We investigate this question empirically by applying Reinforcement Learning (RL) and Supervised Fine-Tuning (SFT) to LLMs of varying scales (0.5B to 7B parameters) and evaluating them across multiple ToM datasets. Our results reveal a scale-dependent impact of RL: while RL significantly improves accuracy and fosters high-quality, interpretable, and transferable belief-tracking reasoning in larger models (7B), it leads to "reasoning collapse" in smaller models ($\leq$3B), where high accuracy and generalization ability are achieved via drastically shortened, less meaningful responses. Surprisingly, further SFT achieves competitive and generalizable performance across these benchmarks, often matching or exceeding RL models in accuracy, despite not being explicitly trained to produce structured reasoning traces. These findings highlight a critical discrepancy between benchmark accuracy and the nature of learned reasoning. Our work suggests that current ToM benchmarks may be solvable without requiring the explicit, human-like simulation of mental states they were designed to probe. LLMs, particularly when scale is limited or training signals focus solely on output correctness, may leverage alternative rules effective for benchmark data structures.

Population-population generalization is a challenging problem in multi-agent reinforcement learning (MARL), particularly when agents encounter unseen co-players. However, existing self-play-based methods are constrained by the limitation of inside-space generalization. In this study, we propose Bidirectional Distillation (BiDist), a novel mixed-play framework, to overcome this limitation in MARL. BiDist leverages knowledge distillation in two alternating directions: forward distillation, which emulates the historical policies' space and creates an implicit self-play, and reverse distillation, which systematically drives agents towards novel distributions outside the known policy space in a non-self-play manner. In addition, BiDist operates as a concise and efficient solution without the need for the complex and costly storage of past policies. We provide both theoretical analysis and empirical evidence to support BiDist's effectiveness. Our results highlight its remarkable generalization ability across a variety of cooperative, competitive, and social dilemma tasks, and reveal that BiDist significantly diversifies the policy distribution space. We also present comprehensive ablation studies to reinforce BiDist's effectiveness and key success factors. Source codes are available in the supplementary material.