Multi-Modal, Multi-Environment Machine Teaching for Robust Reward Learning

🕒 Published (v1): 2026-07-09 16:18 UTC · Source: Arxiv · link

Why this paper was selected

Multi-modal, multi-environment reward learning; addresses alignment robustness for deployed agents

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TL;DR

Reward functions learned from human feedback in a single environment routinely overfit to that environment's dynamics and fail to generalize. This paper theoretically characterizes feedback modality informativeness and proves that reward identifiability is environment-dependent, then introduces HSCOT, a hierarchical machine teaching algorithm that greedily selects diverse environments and heterogeneous feedback modalities to constrain rewards across multiple MDPs.

Problem

Existing machine teaching for inverse reinforcement learning (IRL) is confined to single-environment, demonstration-only settings. Because demonstrations in one MDP entangle reward information with that MDP's transition structure, learned reward parameters \(w\) overfit to environment-specific dynamics and produce high regret when deployed elsewhere. No prior framework jointly analyzes how heterogeneous feedback modalities and environment diversity together constrain reward generalization.

Method

The paper assumes linear rewards \(R_w(s,a) = w^\top \phi(s,a)\) and unifies all feedback types (demonstrations, pairwise comparisons, corrections, emergency stops) as linear preference constraints \(w^\top \Delta\Phi \geq 0\) in the high-rationality limit \(\beta \to \infty\), where \(\Delta\Phi = \Phi(\xi^+) - \Phi(\xi^-)\).

The feasible reward space for a dataset \(D\) is the generalized behavioral equivalence class: $\(\text{gBEC}(D) = \{w \in \mathbb{R}^d \mid w^\top \Delta\Phi \geq 0,\ \forall \Delta\Phi \in \Delta\Phi(D)\}.\)$

Reward ambiguity is quantified by \(G(D) = \text{Volume}(\text{gBEC}(D))\).

HSCOT (Hierarchical Set Cover Optimal Teaching) operates in two nested levels: 1. Outer level — greedily selects a set of MDPs whose feature-difference spans \(V_k = \text{span}\{\Delta\Phi(\xi^+,\xi^-)\}\) expose complementary constraint directions, framed as a set-cover problem over uncovered reward dimensions. 2. Inner level — within each selected MDP, strategically queries low-cost feedback instances (choosing modality based on the budget regime) to maximally shrink the remaining gBEC.

Key Contributions

• Formal proof that in the unlimited-data regime, comparison feedback produces the strictly smallest feasible region: \(H_\text{comparison} \subsetneq H_\text{demo} \subsetneq H_\text{correction} \subsetneq H_\text{E-stop}\) (Propositions 1–3).
• Proof that under finite budgets the ordering reverses: demonstrations are more constraint-efficient per query because each demonstration implicitly enforces all optimality constraints at a visited state simultaneously.
• Theorem 1: Even unlimited feedback within a single MDP \(M_k\) leaves reward ambiguity in directions outside the feature-difference span \(V_k\); resolving it requires at least one additional MDP whose span covers the missing directions.
• HSCOT, the first framework to jointly optimize environment selection and heterogeneous feedback selection for IRL teaching.
• Empirical demonstration that HSCOT achieves higher constraint coverage and substantially lower regret on held-out environments than uniform teaching under identical feedback budgets.

Results

• HSCOT achieves higher gBEC constraint coverage compared to uniform teaching baselines (environments selected randomly or feedback queried uniformly) under identical total feedback budgets.
• HSCOT achieves substantially lower regret on held-out environments than uniform baselines.
• Feasibility heatmaps confirm the finite-data regime ordering (demonstrations most efficient per query) and the unlimited-data regime ordering (comparisons tightest globally).
• (Note: the provided text is truncated before the full quantitative experiment tables; specific numeric regret values are not available in the excerpt.)

Limitations

• Assumes linear reward parameterization \(R_w = w^\top\phi\); non-linear reward classes are not analyzed.
• Theoretical guarantees use the high-rationality limit (\(\beta \to \infty\)); noisy, sub-rational human feedback is not modeled in the teaching optimality proofs.
• HSCOT requires access to a library of diverse MDPs at teaching time, which may be impractical when environments cannot be simulated or enumerated in advance.
• Set-cover-based environment selection is greedy and does not guarantee global optimality.
• E-stop constraints are proven to be trajectory-local (Lemma 1), making them weak; the paper largely treats E-stops as a lower-tier modality but does not propose alternatives for safety-critical online settings where E-stops are the only available signal.

Relevance to Agentic AI / LLM Agents

This paper directly addresses the reward generalization problem that underlies robust agent alignment: an agent trained from human feedback in one context must not have its objective entangled with that context's dynamics when deployed elsewhere. The gBEC framework and HSCOT provide principled, teacher-centric tools for structuring RLHF data collection — selecting which environments to elicit feedback in and which feedback modality to use — rather than passively aggregating whatever feedback is available. For multi-environment or continually redeployed LLM agents (e.g., tool-use agents operating across heterogeneous APIs or embodied robots across layouts), the insight that reward ambiguity is structurally environment-dependent, not just a data-quantity problem, has direct implications for how alignment datasets should be curated. The unified gBEC formalism connecting demonstrations, comparisons, corrections, and E-stops also provides a theoretical foundation for mixing RLHF feedback types that is absent from most current LLM alignment practice.