Optimistic Policy Regularization

On-policy reinforcement learning methods, like Trust Region Policy Optimization (TRPO) and Proximal Policy Optimization (PPO), often demand extensive data per update, leading to sample inefficiency. This paper introduces Reflective Policy Optimization (RPO), a novel on-policy extension that amalgamates past and future state-action information for policy optimization. This approach empowers the agent for introspection, allowing modifications to its actions within the current state. Theoretical analysis confirms that policy performance is monotonically improved and contracts the solution space, consequently expediting the convergence procedure. Empirical results demonstrate RPO's feasibility and efficacy in two reinforcement learning benchmarks, culminating in superior sample efficiency. The source code of this work is available at https://github.com/Edgargan/RPO.

Proximal policy optimization (PPO) approximates the trust region update using multiple epochs of clipped SGD. Each epoch may drift further from the natural gradient direction, creating path-dependent noise. To understand this drift, we can use Fisher information geometry to decompose policy updates into signal (the natural gradient projection) and waste (the Fisher-orthogonal residual that consumes trust region budget without first-order surrogate improvement). Empirically, signal saturates but waste grows with additional epochs, creating an optimization-depth dilemma. We propose Consensus Aggregation for Policy Optimization (CAPO), which redirects compute from depth to width: $K$ PPO replicates are optimized on the same batch, differing only in minibatch shuffling order, and then aggregated into a consensus. We study aggregation in two spaces: Euclidean parameter space, and the natural parameter space of the policy distribution via the logarithmic opinion pool. In natural parameter space, the consensus provably achieves higher KL-penalized surrogate and tighter trust region compliance than the mean expert; parameter averaging inherits these guarantees approximately. On continuous control tasks, CAPO outperforms PPO and compute-matched deeper baselines under fixed sample budgets by up to 8.6x. CAPO demonstrates that policy optimization can be improved by optimizing wider, rather than deeper, without additional environment interactions.

Among on-policy deep reinforcement learning methods, Proximal Policy Optimization (PPO) has become the de facto standard, due to its consistently strong empirical performance across diverse application domains. However, on-policy methods are inherently sample inefficient: fresh data collected under the current policy is used for just a few updates before being discarded. Off-policy methods avoid this inefficiency via experience replay, achieving notable sample efficiency gains, but at the cost of training instabilities or extensive tuning. This motivated the rise of hybrid strategies that augment PPO with off-policy data reuse. Existing sample-reuse variants of PPO demonstrated improved sample efficiency over vanilla PPO, yet a systematic study of when reuse helps, in which scenarios, and to what extent remains missing. In this work, we study the effectiveness of sample reuse in PPO by instantiating two variants within a multiple importance weighting framework. Both retain the core PPO mechanics, reusing only samples from a window of recent iterations, thereby isolating the effect of data reuse from other factors. The variants, termed wPPO-U and wPPO-BH, employ vanilla importance weights or balance-heuristic-corrected ones, respectively. For both, we derive policy improvement lower bounds providing theoretical grounding for their respective losses. We use them to empirically study when and how data reuse improves sample efficiency or final performance of PPO across continuous control tasks.