When Learning Rates Go Wrong: Early Structural Signals in PPO Actor-Critic

Activation functions are what make deep networks expressive: without them, the model collapses to a linear map. Yet we still evaluate training mostly from the outside, through loss, accuracy, return, or final calibration, while the internal structural evolution of the network remains largely unobserved. In this paper, we argue that the Overfitting--Underfitting Indicator (OUI) should be understood as a first practical observable of that internal structure. Across our recent results, OUI consistently appears as an early, label-free, activation-based signal that reveals whether a network is entering a poor or promising training regime before convergence. In supervised learning, it anticipates weight decay regimes; in reinforcement learning, it discriminates learning-rate regimes early in PPO actor--critic; and in online control, it can drive layer-wise weight decay adaptation. Read together with recent evidence that activation patterns tend to stabilize earlier than parameters, these results suggest a broader research direction: an activation-centric theory of training dynamics. OUI is becoming an empirical foothold toward this theory.

Despite its widespread use, Proximal Policy Optimization with clipping (PPO-Clip) remains difficult to tune, and the interactions among critic learning, clipping, and rollout reuse remain incompletely understood. We develop a non-asymptotic analysis of PPO-Clip as a closed-loop actor--critic system. It captures actor--critic coupling, nonsmooth probability-ratio clipping, finite-batch reuse, and predictable early stopping under explicit coverage and critic regularity assumptions, using raw GAE and Monte Carlo critic targets. Our synchronous and asynchronous guarantees jointly characterize policy stationarity and the tracking accuracy of the learned critic, with explicit dependence on algorithmic parameters. A sufficient coupling condition gives optimization, critic tracking, clipping, and finite-batch errors a common amplification bound. The asynchronous result also requires a delay-dependent critic stepsize restriction; violating these conditions does not establish divergence. For finite layered MDPs with tabular critics, a uniform bound on the actual clipped-gradient class replaces complete-trajectory counting. A verified growing-horizon family has polynomial sample complexity, and a two-time-scale schedule gives $O(T^{-2/5})$ stationarity and critic-tracking bounds with explicit fresh-rollout accounting. These results together advance our understanding about PPO and provide theoretical guidance in tuning.

An agent's performance stagnating at a suboptimal level is a common problem in deep on-policy RL. Focusing on PPO, we show that plateaus in certain regimes arise not because of known exploration, capacity, or optimisation challenges, but because sample-based estimates of the loss eventually become poor proxies for the true objective over the course of training. Looking deeper, PPO alternates between sampling rollouts from several parallel environments online using the current policy (which we call the "outer loop") and performing repeated minibatch SGD steps against this offline dataset (the "inner loop"). In our work, we abstract away the inner loop, and conceptually model the outer loop as standard stochastic optimisation. The step size is then controlled by the regularisation strength towards the previous policy and the gradient noise by the number of samples collected between policy update steps. This framing predicts that, much like in SGD, if the outer step size is too large relative to the noise, updates become uninformative and lead to the policy thrashing around a local optimum instead of converging. Recasting PPO in this light makes it clear that there are two ways to address this particular type of learning stagnation: either reduce the step size or increase the number of samples collected between updates. We validate the predictions of our model and conclude that increasing the number of parallel environments is a simple way to avoid these plateaus by simultaneously altering both these factors. Applying our analysis and scaling PPO to more than 1M parallel environments enables monotonic performance improvement up to one trillion transitions and leads to vastly superior performance compared to prior baselines in a complex open-ended domain.