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A theoretical case-study of Scalable Oversight in Hierarchical Reinforcement Learning

NeurIPS 2024 · Reinforcement learning › Visual and representation RL · approach: Subgoal generation for hierarchical RL · 1 citations (OpenAlex)

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Theoretical study of scalable oversight in goal-conditioned hierarchical RL: a sublinear-regret UCB algorithm (Hier-UCB-VI) for cardinal feedback and a hierarchical experiment-design algorithm (Hier-REGIME) for preference feedback, with no experiments.

Problem

How to scale bounded human feedback to supervise model outputs too large for labelers to evaluate in full, using the hierarchical structure of outputs in goal-conditioned hierarchical RL.

Approach

Use goal-conditioned hierarchy so that humans only rate sub-MDP trajectories of bounded length; add a goal-reachability term to the sub-MDP reward so low-level policies land at goal states, enabling the high-level MDP transitions to be idealized and yielding regret decomposing additively over sub-MDPs. For preferences, use hierarchical experiment design with low- or high-level comparisons, with id

Key results

• Hier-UCB-VI achieves sublinear regret, with cumulative regret bound of order sqrt(K) under UCB-VI subroutine (Theorem 1, Corollary 3).
• Under ordinal feedback, low-level feedback alone is insufficient: a non-identifiability result shows regret constant in the number of low-level samples (Proposition 1).
• Corollary 1 gives sample-complexity rates: idealized feedback O(N_l^-1/4 + N_h^-1/2), current feedback O(N_l^-1/2 + N_h^-1/2), and low-level-only O(N_l^-1/2) when coverage is sufficient.

Measured effects reported in the paper

Surprising findings

• Low-level ordinal feedback alone cannot identify the optimal high-level policy, so regret stays non-vanishing regardless of low-level sample size.
• Idealized high-level feedback (assuming perfect sub-policy execution) introduces bias that slows the rate to N_l^-1/4 relative to the unbiased current-feedback rate.

Limitations

• Regret guarantees are relative to the optimal hierarchical policy, so performance depends on the quality of the given goal function, which is assumed rather than learned.
• Theoretical only; no empirical experiments are reported.
• Assumes linear reward parametrization and that labelers can assess high-level outputs under idealized or current sub-policy execution.

Experimental setup

Metrics: regret sample complexity

Builds on: UCB-VI REGIME Bradley-Terry-Luce preference model options framework sub-MDP learning (Mann et al.)

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