Selective Agent Guidance via Entropy: Learning Autonomous Policies from Imperfect VLM Teachers

Vision-Language Models (VLMs) provide useful priors for interactive decision-making, but using them directly as policies is expensive and brittle: they must be queried at every step, do not improve from environment interaction, and can repeat systematic errors. We study how to learn a cheap autonomous policy from an online, expensive, and imperfect but informative VLM teacher. We propose SAGE (Selective Agent Guidance via Entropy), a framework that queries a VLM only when the learner is uncertain, executes the suggested action during training, and distills guidance into a lightweight Reinforcement Learning (RL) policy. Because VLM advice is not always reliable, SAGE can weight teacher-action distillation using environment-derived advantages rather than treating all suggestions as equally useful. Across sparse-reward visual reasoning and navigation tasks, SAGE learns policies that act without VLM guidance at evaluation time and improves over unguided RL in several environments, including settings where the learned policy exceeds its VLM teacher. The results show that selective guidance is most beneficial when the VLM can help the agent discover high-reward trajectories, and less useful when unguided exploration already succeeds or teacher actions do not lead to informative experience. SAGE also reduces VLM usage by prompting the teacher only on a fraction of training steps and requiring no VLM calls at deployment. Overall, our results suggest that VLMs don't need to be used as fixed policies to be useful; they can instead act as temporary, imperfect sources of guidance whose value is tested and internalized through interaction.

Adaptive Mixing of Policies from Searching and Policies from Learning

Background: Distillation of training targets generated thru search/planning has proven useful in reinforcement learning, but search can take exceedingly long. Objectives: Rather than perform search to the same depth every time (typically at a fixed period of steps), reduce the search depth proportionally to the quality of the policy network priors. Methods: We describe Flexer, an architecture that, for each step, mixes the policy from a neural network and the policy from Monte Carlo tree search. The mixing factor favors the MCTS policy as the policy imitation error of the network and the environment models' variance increases. Results: Flexer outperforms a version of AlphaZero (and DQN and ADP) for some experiments on three toy symbolic problems.

Interpretable reinforcement learning with decision-tree pruning

Reinforcement learning policies are difficult to inspect, but interpreting them is a prerequisite for trustworthiness. Converting a trained policy into explicit decision-tree rules improves transparency and the resulting artifacts often remain too complex for human understanding. We present a pruning process that simplifies such rule-based policies while preserving task performance and making edits to the policy auditable. The process defines a small set of structural and usage-aware operators and evaluates candidate edits by re-executing the policy to measure return and interpretability proxies. This exposes an transformation process from complex to compact policy structures. We investigate this approach on classic control and MuJoCo benchmarks, where pruning traces reveal consistent interpretability improvements while maintaining high performance.

SMOPD: Multi-Reward Reinforcement Learning via Specialize-and-Merge Online Policy Distillation

We aim to improve model performance in multi-reward reinforcement learning training process. Existing Group reward-Decoupled Normalization Policy Optimization (GDPO) has mitigated the issue of reward signals masking one another during direct scalarization by normalizing each reward dimension separately before aggregation. However, our experiments show that GDPO still struggles to balance reward signals with different granularities. Specifically, in some particular training tasks, the model may receive a dense reward that assigns fine-grained scores ranging from 0.1 to 1.0, together with a sparse reward that provides only binary feedback of either 0 or 1. In such cases, we find that the sparse reward may provide an insufficient optimization signal, preventing its corresponding capability from being effectively reinforced. Therefore, how can we strengthen the optimization signal from the sparse reward without sacrificing the capability already learned from the fine-grained reward? To overcome this limitation, we propose Specialize-and-Merge Online Policy Distillation (SMOPD), a two-stage training method for multi-reward optimization. Stage1-Specialize: SMOPD first employs reward-priority configurations to train multiple reward-specialized teachers, allowing each reward to be learned under conditions where its signal can effectively drive optimization. Stage2-Merge: SMOPD then utilizes online policy distillation to combine the reward-specialized capabilities of these teachers into a single student policy, while maintaining balanced task-level optimization. To validate our method, we conduct experiments on two multi-reward settings: complementary rewards(tool-calling accuracy and format) and conflicting rewards (helpful and harmless rewards). Based on above settings, SMOPD outperforms GDPO across 1.5B, 3B and 7B backbones.

Beyond the Best Teacher: Expanding and Compressing the Reasoning Solution Manifold

A single reinforcement-learning run can produce a strong reasoner yet an incomplete teacher: it often amplifies only a subset of the valid solution modes. We argue that reinforcement learning (RL)-trained policies should therefore be viewed as local probes of a multi-basin reasoning solution manifold, rather than as globally reliable supervisors. Based on this view, we propose an expand-then-compress framework that couples teacher construction with multi-teacher policy distillation. In the expansion stage, Residual Group Relative Policy Optimization (RGRPO) trains a sequence of teachers from a common initialization and redirects each later round toward examples not yet covered by the accumulated teacher union. In the compression stage, reliability-gated Teacher-Union On-policy Distillation (TU-OPD) lets the student learn from its own response prefixes. For each example, only reliable teachers contribute, and their sampled-token OPD losses are weighted by their per-example quality. We further introduce Consensus-Residual Decomposition, which preserves a winner teacher's excess token preferences over its reliable peers, preventing specialist behavior from being suppressed during teacher aggregation. Experiments on mathematical reasoning, code generation, and instruction following show that the resulting Qwen3-1.7B student consistently outperforms the strongest individual teacher across all three domains, yielding relative improvements of 2.0%, 8.3%, and 6.9%, respectively, while retaining single-model inference. These results establish a simple but powerful principle: stronger students can be obtained not by selecting a single better teacher, but by deliberately constructing and compressing a complementary teacher union.

Explainable Reinforcement Learning via Physics-Aware Policy Distillation

In safety-critical sectors such as robotics and automotive engineering, the deployment of Deep Reinforcement Learning (DRL) is often hindered by the black-box nature of deep neural networks. This lack of transparency poses significant challenges for regulatory compliance and human-agent trust. This paper presents an experimental study aimed at making high-performance continuous control DRL systems interpretable. A policy distillation framework is implemented using the classic Inverted Pendulum benchmark. A high-performance Twin Delayed DDPG (TD3) agent serves as an opaque, continuous teacher model, whose policy is distilled into an interpretable student surrogate based on a shallow Decision Tree. By leveraging a custom physics-aware feature and "Noisy Oracle Rollouts" for dataset generation, the distillation process achieves performance equivalent to the expert teacher. Furthermore, comparative control theory analysis reveals a fundamental trade-off: transitioning from continuous to discrete rule-based control induces high-frequency Bang-Bang actuation and a stable bimodal limit cycle. Simulation results indicate that Bounded-Input Bounded-Output (BIBO) stability is maintained while providing both global and local interpretability for safe autonomous systems.

From Black Box to Executable Logic: Explainable Reinforcement Learning through Prolog Expert Systems

A trained deep reinforcement learning policy is a black box, and we ask whether it can be made explainable by rewriting it as an executable logic program that reproduces its behaviour and that a person can read, a logic engine can run, and an optimizer can edit. We present a three-stage post-hoc transformation that extracts a frozen proximal policy optimization teacher, induces an ordered rule list from its decisions in the manner of classical relational learning, and emits the result as a Prolog program whose every decision is executed by an off-the-shelf logic engine; a subsequent expansion stage edits the rule base and accepts an edit only when policy evaluation certifies a return increase. We prove four guarantees. A return-loss bound makes the distilled program a machine-checkable certificate in a finite Markov decision process, and the expansion loop improves monotonically and terminates. For the continuous-observation setting we answer whether the conversion is possible at all: the propositional threshold instantiation converts the network to arbitrary fidelity as the resolution B grows, with disagreement O(1/B) and a return gap that closes at the same rate, and a matching lower bound shows the cost is exponential in the observation dimension for an oblique decision boundary. Empirically, on a two-room key-and-door task with 16,944 reachable states the expanded Prolog program attains exact optimal return in every seed and, in a budget-capped regime, exceeds the stochastic teacher on exact return in ten of ten seeds. On three continuous-control tasks the emitted program substitutes the network, matching the neural teacher within noise on Acrobot with eleven clauses and recovering about 97% of its return on CartPole, while on the finer-control LunarLander it recovers only partially, exactly the ceiling the exponential lower bound predicts.

ORCAID: Oblique Rule-Based Continuous-Action Interpretation for Deep RL Policies

Explainability remains a key issue in reinforcement learning (RL). Distilling an interpretable policy from an agent trained in a complex environment is particularly challenging when the action space is continuous. We introduce ORCAID, a novel method for extracting interpretable rule-based policies from RL agents operating in mixed continuous-discrete environments with continuous action spaces. Our main contribution is an efficient oblique decision tree training algorithm that partitions the state space by hyperplanes and fits local linear models. The key idea lies in a three-stage split search: efficient random initialization, local refinement, and backward elimination. Finally, adjacent leaves are merged to yield a concise set of interpretable rules describing a given deep RL policy. We evaluate ORCAID across multiple RL environments, demonstrating that the extracted rule-based policies maintain strong performance with a low number of parameters and can even be used to improve the performance of the original deep RL policy.

Self-Review Reinforcement Learning (SRRL) with Cross-Episode Memory and Policy Distillation

Reinforcement Learning is commonly used to train large language models using environmental feedback. In applied settings, the environment usually provides sparse or delayed feedback. This makes it difficult for the model to pinpoint which actions in its reasoning led to success or failure. So, learning effectively from these signals is hard because the model must determine how each failure should inform meaningful behavioral corrections in subsequent iterations. We introduce a training framework, Self-Review Reinforcement Learning, that embeds an explicit self-review step into each RL episode. When a first-pass response fails, the model generates a self-review to identify what went wrong, which conditions an improved second attempt. Unlike inference-time reflection approaches, such as Reflexion, the framework optimizes self-review with policy gradients and internalizes improvements into the base policy via selective distillation, ensuring they persist across future episodes. A cross-episode memory keeps successful self-reviews for reuse when encountering similar tasks in future episodes during training. We evaluate SRRL against a standard RLVR baseline using the GRPO optimizer across two language models, Qwen 3-4B and OLMo-3- 7B, on GSM8K benchmark. SRRL consistently outperforms the RLVR in final reward performance and achieves greater learning efficiency by successfully transforming feedback into behavioral improvement.

Trust Region Policy Distillation

Big goals are hard to achieve all at once; breaking them into small steps is wiser. We present Trust Region Policy Distillation (TOP-D), which transforms the notoriously unstable, high-variance On-Policy Distillation (OPD) into a stable training paradigm by dynamically constructing a proximal teacher. Theoretically, we establish a rigorous framework demonstrating that TOP-D inherently controls gradient variance. By providing a formal global convergence analysis alongside a monotonic improvement bound, we mathematically formalize the reliability and stability of the overall training dynamics. Empirically, TOP-D dramatically enhances training stability, sample efficiency, and final performance on mathematical reasoning tasks. More importantly, TOP-D introduces zero additional computational overhead, positioning itself as a promising alternative to the well-established OPD paradigm.

Discovering Interpretable Multi-Parameter Control Policies for Evolutionary Algorithms Using Deep Reinforcement Learning

While deep Reinforcement Learning (deep-RL) has been increasingly applied to parameter control in evolutionary algorithms, rigorous theoretical analysis of parameter control remains largely restricted to single-parameter settings, owing to the difficulty of deriving effective, interpretable multi-parameter policies amenable to formal study. We demonstrate how deep-RL can be leveraged to overcome this barrier, using the (1+($λ$,$λ$))-genetic algorithm optimizing OneMax, one of the few problems where a super-constant speedup of dynamic control has been formally proven, as a representative case study. We first show that standard approaches struggle to converge in this multi-parameter setting, and introduce algorithm-agnostic enhancements targeting action-space decomposition, reward shifting, and long-horizon discounting. With these in place, we compare common deep-RL methods and find that Double Deep Q-Networks uniquely avoid the policy collapse observed in Proximal Policy Optimization, yielding trajectories suitable for downstream analysis. Crucially, we move beyond the ``black-box'' nature of neural networks by distilling the learned behaviors into a transparent, symbolic control policy. This resulting policy does not only offer interpretability for future theoretical analysis but also yields exceptional performance, consistently outperforming existing baselines across a wide range of problem sizes.