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Optimistic Task Inference for Behavior Foundation Models

Thomas Rupf, Marco Bagatella, Marin Vlastelica, Andreas Krause

TL;DR

This paper addresses the data-efficiency bottleneck of Behavior Foundation Models (BFMs) by introducing OpTI-BFM, an online, optimistic method to infer task rewards through environment interaction rather than offline labeling. By leveraging a near-linear relation between rewards, features, and successor features, OpTI-BFM maintains a least-squares estimate of the task embedding and uses confidence sets to select informative task embeddings, achieving sublinear regret in an episodic linear-bandit-style setting. The authors provide a formal regret bound, present practical variants including Thompson Sampling and non-stationary reward adaptation, and demonstrate that OpTI-BFM identifies unseen reward functions within a handful of episodes on standard benchmarks, often matching or surpassing offline reward-inference baselines. The work bridges BFMs and linear-bandit theory, enabling efficient, data-light task inference with potential applicability to pixel-based reward learning and broader online RL scenarios.

Abstract

Behavior Foundation Models (BFMs) are capable of retrieving high-performing policy for any reward function specified directly at test-time, commonly referred to as zero-shot reinforcement learning (RL). While this is a very efficient process in terms of compute, it can be less so in terms of data: as a standard assumption, BFMs require computing rewards over a non-negligible inference dataset, assuming either access to a functional form of rewards, or significant labeling efforts. To alleviate these limitations, we tackle the problem of task inference purely through interaction with the environment at test-time. We propose OpTI-BFM, an optimistic decision criterion that directly models uncertainty over reward functions and guides BFMs in data collection for task inference. Formally, we provide a regret bound for well-trained BFMs through a direct connection to upper-confidence algorithms for linear bandits. Empirically, we evaluate OpTI-BFM on established zero-shot benchmarks, and observe that it enables successor-features-based BFMs to identify and optimize an unseen reward function in a handful of episodes with minimal compute overhead. Code is available at https://github.com/ThomasRupf/opti-bfm.

Optimistic Task Inference for Behavior Foundation Models

TL;DR

This paper addresses the data-efficiency bottleneck of Behavior Foundation Models (BFMs) by introducing OpTI-BFM, an online, optimistic method to infer task rewards through environment interaction rather than offline labeling. By leveraging a near-linear relation between rewards, features, and successor features, OpTI-BFM maintains a least-squares estimate of the task embedding and uses confidence sets to select informative task embeddings, achieving sublinear regret in an episodic linear-bandit-style setting. The authors provide a formal regret bound, present practical variants including Thompson Sampling and non-stationary reward adaptation, and demonstrate that OpTI-BFM identifies unseen reward functions within a handful of episodes on standard benchmarks, often matching or surpassing offline reward-inference baselines. The work bridges BFMs and linear-bandit theory, enabling efficient, data-light task inference with potential applicability to pixel-based reward learning and broader online RL scenarios.

Abstract

Behavior Foundation Models (BFMs) are capable of retrieving high-performing policy for any reward function specified directly at test-time, commonly referred to as zero-shot reinforcement learning (RL). While this is a very efficient process in terms of compute, it can be less so in terms of data: as a standard assumption, BFMs require computing rewards over a non-negligible inference dataset, assuming either access to a functional form of rewards, or significant labeling efforts. To alleviate these limitations, we tackle the problem of task inference purely through interaction with the environment at test-time. We propose OpTI-BFM, an optimistic decision criterion that directly models uncertainty over reward functions and guides BFMs in data collection for task inference. Formally, we provide a regret bound for well-trained BFMs through a direct connection to upper-confidence algorithms for linear bandits. Empirically, we evaluate OpTI-BFM on established zero-shot benchmarks, and observe that it enables successor-features-based BFMs to identify and optimize an unseen reward function in a handful of episodes with minimal compute overhead. Code is available at https://github.com/ThomasRupf/opti-bfm.
Paper Structure (50 sections, 8 theorems, 77 equations, 13 figures, 2 tables, 1 algorithm)

This paper contains 50 sections, 8 theorems, 77 equations, 13 figures, 2 tables, 1 algorithm.

Key Result

Proposition 1

(informal) Under assumptions A1-A4, in an episodic discounted MDP, if OpTI-BFM (alg:ours) only updates $z_t$ at the start of each episode, it incurs an expected regret of $R_n \le \tilde{\mathcal{O}}\left(d\sqrt{n}\right)$.

Figures (13)

  • Figure 1: In contrast to the standard offline task inference pipeline for BFMs, we explore an alternative online framework: instead of producing a point-estimate of the task embedding from an existing dataset, we actively collect data to build a belief over task embeddings, which results in milder labeling requirements and fast retrieval of a near-optimal policy.
  • Figure 2: Mean relative performance over 10 episodes of interaction in DMC. OpTI-BFM recovers Oracle performance in 5 episodes. We report per-task absolute performance in \ref{['fig:main-ext']} in \ref{['sec:more-exp']}.
  • Figure 3: Relative performance after different # of environment interactions. OpTI-BFM is consistently among the top performers for all environments and time-steps. We show per task performance in \ref{['fig:data-ext']} in \ref{['sec:more-exp']}.
  • Figure 4: Relative performance of our methods, and their variants that keep task embeddings fixed for each episode (-EP). Updating the task embedding during the episode leads to faster convergence. For longer episode evaluations see \ref{['fig:ep']} in \ref{['sec:more-exp']}.
  • Figure 5: Horizontal velocity of OpTI-BFM in our custom velocity tracking tasks in DMC Walker for different decay rates $\rho$. OpTI-BFM can adapt to non-stationary reward functions when decaying the weight of old observations.
  • ...and 8 more figures

Theorems & Definitions (16)

  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Proposition 3
  • proof
  • Proposition 4
  • proof
  • Theorem 1
  • Proposition 5
  • ...and 6 more