Actor-Accelerated Policy Dual Averaging for Reinforcement Learning in Continuous Action Spaces

Actor-critic methods reuse past experience to improve sample efficiency. However, historical data are typically regarded as off-policy samples for the current policy-improvement update. This work introduces Regularized Dual Averaging Actor Critic (RDA2C), which assigns a distinct role to replay. In regularized dual averaging, the subsequent policy is determined by accumulated policy-improvement feedback, so historical advantage estimates contribute directly to the actor objective rather than solely to the most recent update. RDA2C stores state-action samples with critic-estimated advantage labels, fits a dual score model $Z_θ$ to the aggregated dataset, and derives the current policy from the accumulated score model using the entropy mirror map. In this way, replay defines an empirical dual objective from which the policy is computed. To analyze RDA2C, we establish a finite-time value-gap decomposition, separating the regularized dual-averaging term from errors due to stale-replay supervised fitting, critic bias, finite-buffer variance, and replay coverage, and stating the assumptions under which each error is bounded. RDA2C accepts advantage labels from any critic. With GAE labels, RDA2C outperforms PPO on six of eight MuJoCo tasks and eight of twelve Atari games. RDA2C also outperforms AAPDA, the closest dual-averaging baseline, on six of eight MuJoCo tasks. With twin-$Q$ labels, RDA2C matches SAC at matched batch size and update frequency.

The framework of robust Markov decision processes (RMDPs) allows the design of reinforcement learning agents that satisfy performance guarantees under worst-case transition dynamics. Traditional RMDPs consider discrete-time dynamics and recently, sample-efficient policy gradient algorithms have been considered in this context. This paper investigates policy gradient algorithms within a continuous-time RMDP framework. Policy gradients and adversarial gradients are derived using pathwise and adjoint-based formulas for stochastic and ordinary differential equations. We propose double-loop optimisers to obtain linear convergence in the oracle-based setting and an $\tilde{\mathcal{O}}(\frac{1}{ε^2})$ sample complexity in the sample-based setting in an analysis which also derives novel tools for the framework of undiscounted total cost MDPs. Additionally, we propose mean-field optimisers as distributional optimisers with an $\tilde{\mathcal{O}}(\frac{1}{K})$ oracle-based convergence rate and an $\tilde{\mathcal{O}}(\frac{N^2}ε)$ sample complexity under $N$-particle approximation. The effectiveness of continuous-time policy gradient algorithms is confirmed for both optimisers on continuous-time RMDPs with neural ordinary differential equation dynamics.

Distributed training and increasing the gradient update frequency are practical strategies to accelerate learning and improve performance, but both exacerbate a central challenge: policy lag, which is the mismatch between the behavior policy generating data and the learning policy being updated. Policy lag can hinder the scaling of on-policy learning algorithms to larger problems. In this paper, we identify the sources of policy lag caused by distributed learning and high update frequency. We use the findings to propose total Variation-based Advantage aligned Constrained policy Optimization (\methodacronym) as a practical approach to mitigate policy lag. We empirically validate our method and show that it offers better robustness to policy lag in classic RL tasks and a modern RL for LLM math reasoning task.