Beyond Reward Hacking: Proxy Divergence Across Four Layers of a Staged Humanoid Learning Pipeline

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Article Summary

A reinforcement-learning (RL) pipeline for a legged robot is assembled from proxies. A reward stands in for intended behaviour, a curriculum gate stands in for competence, an evaluation statistic stands in for robustness, and a reference motion stands in for an achievable skill. The traditional view treats only the first of these as optimised against, and so locates specification failure (reward hacking) in the reward alone. I argue that all four are proxies in the same formal sense, that each has a characteristic divergence mechanism, and that each admits a reformulation that closes it. For every layer I state the traditional formulation, derive the condition under which it diverges from its target, and give the alternative: first-order (L1) costs where quadratic kernels are flat, peak and outcome statistics where curriculum gates average, gate reachability and information checks, deterministic and phase-desynchronised evaluation, curriculum state treated as part of the model, feasibility-first reference design with residual feed-forward, and function-preserving input widening that lets one policy grow instead of being retrained. The arguments are illustrated by measurements from one continuous lineage of a PPO policy for a simulated 1.91 m humanoid, grown over four stages and 13,500 iterations on a single laptop GPU. Among them, a curriculum gate built on averaged error advanced at its rate limit on every check while the skill it gated was absent, and a batched push test whose synchronised resets aliased the gait phase ranked a 0.5 m/s push as more dangerous than a 2.0 m/s one.

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