Where-to-Learn: Analytical Policy Gradient Directed Exploration for On-Policy Robotic Reinforcement Learning

In reinforcement learning (RL), agents benefit from exploration only because they repeatedly encounter similar states: trying different actions can improve performance or reduce uncertainty; without such retries, a greedy policy is optimal. We formalize this intuition with ReMax, an objective that evaluates a policy by the expected maximum return over $M$ samples, where $M$ is a positive integer, while accounting for return uncertainty. Optimizing this objective induces stochastic exploration as an emergent property, without explicit bonus terms. For efficient policy optimization, we derive a new policy-gradient formulation for ReMax and introduce ReMax PPO (RePPO), a PPO variant that optimizes ReMax while generalizing the discrete retry count $M$ to a continuous parameter $m > 0$, enabling fine-grained control of exploration. Empirically, RePPO promotes exploration, without any explicit exploration bonuses, on the MinAtar and Craftax benchmarks.

Reinforcement learning (RL) has achieved strong performance in robotic control; however, state-of-the-art policy learning methods, such as actor-critic methods, still suffer from high sample complexity and often produce physically inconsistent actions. This limitation stems from neural policies implicitly rediscovering complex physics from data alone, despite accurate dynamics models being readily available in simulators. In this paper, we introduce a novel physics-informed RL framework, called PIPER, that seamlessly integrates physical constraints directly into neural policy optimization with analytical soft physics constraints. At the core of our method is the integration of a differentiable Lagrangian residual as a regularization term within the actor's objective. This residual, extracted from a robot's simulator description, subtly biases policy updates towards dynamically consistent solutions. Crucially, this physics integration is realized through an additional loss term during policy optimization, requiring no alterations to existing simulators or core RL algorithms. Extensive experiments demonstrate that our method significantly improves learning efficiency, stability, and control accuracy, establishing a new paradigm for efficient and physically consistent robotic control.

With massively parallel simulation, on-policy Reinforcement Learning methods such as PPO have become standard in many domains. However, learning from scratch is sample-inefficient and fails to exploit the potential existence of a suboptimal expert, such as a heuristic, a model-based controller, or a policy trained on a related task. Such an expert is often available and can guide early training, but its sub-optimality limits final performance. The challenge then becomes balancing expert guidance against learning from rewards. Existing methods set the expert's influence through a blending weight, a schedule, or an evaluation-driven curriculum. Alternatively, they adapt it with additional learned components such as critics over expert actions or auxiliary agents. However, none optimizes it using the same on-policy objective as the policy itself. We propose a method in which the learner and the expert alternate control within each training episode, and the expert's share of control is a single learnable parameter optimized jointly with the policy. The learner benefits from the expert early in training, but its share of control declines as the learner becomes more competent, until eventually vanishing completely. This leaves the learner acting alone and better than the suboptimal expert. We evaluate our method on 34 tasks across two benchmarks, spanning discrete and continuous action spaces, using both learned and model-based experts. Our method improves sample efficiency over guided and unguided baselines while requiring minimal hyperparameter variation. The expert's share decays to zero as the learner improves, vanishing when the expert is no longer useful.