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Probabilistic Performance Guarantees for Multi-Task Reinforcement Learning

Yannik Schnitzer, Mathias Jackermeier, Alessandro Abate, David Parker

TL;DR

This work introduces a probabilistic certification method for multi-task reinforcement learning that yields high-confidence guarantees on a policy’s performance on unseen tasks drawn from an unknown distribution. It couples rollout-based lower confidence bounds for per-task performance with a distribution-level generalisation bound, producing a unified certificate that accounts for both finite task sampling and finite rollout estimation. The approach is algorithm-agnostic, computationally lightweight, and applicable to high-dimensional domains, offering interpretable safety guarantees without requiring exhaustive data. Empirical results across grid-world and continuous-control environments demonstrate soundness and informative certificates at practical data budgets. The framework advances safe deployment of generalist policies by enabling principled, quantitative assurances about zero-shot task generalisation.

Abstract

Multi-task reinforcement learning trains generalist policies that can execute multiple tasks. While recent years have seen significant progress, existing approaches rarely provide formal performance guarantees, which are indispensable when deploying policies in safety-critical settings. We present an approach for computing high-confidence guarantees on the performance of a multi-task policy on tasks not seen during training. Concretely, we introduce a new generalisation bound that composes (i) per-task lower confidence bounds from finitely many rollouts with (ii) task-level generalisation from finitely many sampled tasks, yielding a high-confidence guarantee for new tasks drawn from the same arbitrary and unknown distribution. Across state-of-the-art multi-task RL methods, we show that the guarantees are theoretically sound and informative at realistic sample sizes.

Probabilistic Performance Guarantees for Multi-Task Reinforcement Learning

TL;DR

This work introduces a probabilistic certification method for multi-task reinforcement learning that yields high-confidence guarantees on a policy’s performance on unseen tasks drawn from an unknown distribution. It couples rollout-based lower confidence bounds for per-task performance with a distribution-level generalisation bound, producing a unified certificate that accounts for both finite task sampling and finite rollout estimation. The approach is algorithm-agnostic, computationally lightweight, and applicable to high-dimensional domains, offering interpretable safety guarantees without requiring exhaustive data. Empirical results across grid-world and continuous-control environments demonstrate soundness and informative certificates at practical data budgets. The framework advances safe deployment of generalist policies by enabling principled, quantitative assurances about zero-shot task generalisation.

Abstract

Multi-task reinforcement learning trains generalist policies that can execute multiple tasks. While recent years have seen significant progress, existing approaches rarely provide formal performance guarantees, which are indispensable when deploying policies in safety-critical settings. We present an approach for computing high-confidence guarantees on the performance of a multi-task policy on tasks not seen during training. Concretely, we introduce a new generalisation bound that composes (i) per-task lower confidence bounds from finitely many rollouts with (ii) task-level generalisation from finitely many sampled tasks, yielding a high-confidence guarantee for new tasks drawn from the same arbitrary and unknown distribution. Across state-of-the-art multi-task RL methods, we show that the guarantees are theoretically sound and informative at realistic sample sizes.
Paper Structure (54 sections, 2 theorems, 48 equations, 11 figures, 2 tables)

This paper contains 54 sections, 2 theorems, 48 equations, 11 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Multi-task and meta reinforcement learning.
  4. Single-task guarantees and distribution-free evaluation.
  5. Certificates via learned finite-state models.
  6. MTRL generalisation bounds.
  7. Background
  8. Reinforcement learning.
  9. Multi-task reinforcement learning.
  10. Performance Metrics.
  11. Problem Setting
  12. Illustrative Example
  13. Computing Performance Certificates
  14. Bounding Per-Task Performance
  15. Binary metrics.
  16. ...and 39 more sections

Key Result

Theorem 5.1

Given a policy $\pi$, $n$ i.i.d. sample tasks $\mathbb{M} \coloneqq \{\mathcal{M}_i \sim \mathcal{D}\}_{i=1}^n$, and per-task lower bounds $\tilde{J}^{\beta}_{\mathcal{M}_i}(\pi)$ such that for $\beta \in (0,1)$. For any confidence $1-\delta$, with $\delta \in (0,1)$ and fixed performance threshold $B \in \mathbb{R}$, it holds that where $\varepsilon \in [0,1]$ is the unique solution to the equa

Figures (11)

  • Figure 1: Example distribution of performances $J_{\mathcal{M}}(\pi)$ induced by a task distribution $\mathcal{D}$. Using sampled tasks and rollout-based lower confidence bounds (red brackets) around empirical per-task performance estimates (red dots), our results certify a lower bound on the safety level $S^\pi_{\mathcal{D}}(B)\ge 1-\varepsilon$ for a user-chosen threshold $B$.
  • Figure 2: Navigation example where the slip probability $p$ defines the task. Panel \ref{['fig:simple-grid-c']} reports the true safety level $S_{\mathcal{D}}^\pi(B)$ (dashed) and the certified lower bound $1-\varepsilon$ (solid curve) from Theorem \ref{['thm:bounddiscard']} at confidence $1-\delta = 0.99$ for any performance threshold $B$.
  • Figure 3: Illustration of the effect of the number of sampled tasks $n$ and rollouts per task $m$ on the certificate from Theorem \ref{['thm:bounddiscard']}.
  • Figure 4: Empirical safety (dashed) and certified safety (solid) for trained policies. In BridgeWorld we compare fixed left- vs. right-bridge policies. In Cheetah, Walker, and Zones we vary the number of sampled tasks $n$ and rollouts per task $m$, indicated by $(n,m)$.
  • Figure 5: Environment visualisations.
  • ...and 6 more figures

Theorems & Definitions (4)

  • Definition 4.1: Safety
  • Theorem 5.1: Safety Certificate
  • proof : Proof sketch
  • Theorem 3.1: Scenario bound with probabilistic inner constraints. Restated from DBLP:conf/tacas/SchnitzerAP25