An Approximate Ascent Approach To Prove Convergence of PPO

Proximal Policy Optimization (PPO) is among the most widely used deep reinforcement learning algorithms, yet its theoretical foundations remain incomplete. Most importantly, convergence and understanding of fundamental PPO advantages remain widely open. Under standard theory assumptions we show how PPO's policy update scheme (performing multiple epochs of minibatch updates on multi-use rollouts with a surrogate gradient) can be interpreted as approximated policy gradient ascent. We show how to control the bias accumulated by the surrogate gradients and use techniques from random reshuffling to prove a convergence theorem for PPO that sheds light on PPO's success. Additionally, we identify a previously overlooked issue in truncated Generalized Advantage Estimation commonly used in PPO. The geometric weighting scheme induces infinite mass collapse onto the longest $k$-step advantage estimator at episode boundaries. Empirical evaluations show that a simple weight correction can yield substantial improvements in environments with strong terminal signal, such as Lunar Lander.

Adaptive Kernel Selection for Stein Variational Gradient Descent

A central challenge in Bayesian inference is efficiently approximating posterior distributions. Stein Variational Gradient Descent (SVGD) is a popular variational inference method which transports a set of particles to approximate a target distribution. The SVGD dynamics are governed by a reproducing kernel Hilbert space (RKHS) and are highly sensitive to the choice of the kernel function, which directly influences both convergence and approximation quality. The commonly used median heuristic offers a simple approach for setting kernel bandwidths but lacks flexibility and often performs poorly, particularly in high-dimensional settings. In this work, we propose an alternative strategy for adaptively choosing kernel parameters over an abstract family of kernels. Recent convergence analyses based on the kernelized Stein discrepancy (KSD) suggest that optimizing the kernel parameters by maximizing the KSD can improve performance. Building on this insight, we introduce Adaptive SVGD (Ad-SVGD), a method that alternates between updating the particles via SVGD and adaptively tuning kernel bandwidths through gradient ascent on the KSD. We provide a simplified theoretical analysis that extends existing results on minimizing the KSD for fixed kernels to our adaptive setting, showing convergence properties for the maximal KSD over our kernel class. Our empirical results further support this intuition: Ad-SVGD consistently outperforms standard heuristics in a variety of tasks.