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Robust Trust

Piotr Dworczak, Alex Smolin

TL;DR

The paper develops a robust framework for AI-assisted decision-making when the adviser may be misaligned, formalizing a trust-region (TRS) representation in belief space that maps misaligned signals to safe boundary interpretations via a Bregman-distance projection. It proves the existence of trust region equilibria (TRE) for zero-sum misalignment and derives sharp minimal viable alignment thresholds, including a complete binary-state analysis with interval trust regions and all-or-nothing outcomes in the binary-action case. For richer state spaces, the misaligned adviser optimally selects boundary messages to maximize distance from the truth, yielding potentially non-convex TRS geometries and ball-shaped regions in symmetric settings. The results provide concrete design implications for AI deployment, offering guardrail-based decision protocols and a principled certification method via saddle-point constructions, with future work focused on broader comparative statics and computable trust-region determination. Overall, the work delivers a principled, minimax-based blueprint for safely leveraging AI advice in high-stakes environments while clarifying when and how trust in advice should be bounded.

Abstract

An agent chooses an action using her private information combined with recommendations from an informed but potentially misaligned adviser. With a known alignment probability, the adviser reports his signal truthfully; with remaining probability, the adviser can send an arbitrary message. We characterize the decision rule that maximizes the agent's worst-case expected payoff. Every optimal rule admits a trust region representation in belief space: advice is taken at face value when it induces a posterior within the trust region; otherwise, the agent acts as if the posterior were on the trust region's boundary. We derive thresholds on the alignment probability above which the adviser's presence strictly benefits the agent and fully characterize the solution in binary-state as well as binary-action environments.

Robust Trust

TL;DR

The paper develops a robust framework for AI-assisted decision-making when the adviser may be misaligned, formalizing a trust-region (TRS) representation in belief space that maps misaligned signals to safe boundary interpretations via a Bregman-distance projection. It proves the existence of trust region equilibria (TRE) for zero-sum misalignment and derives sharp minimal viable alignment thresholds, including a complete binary-state analysis with interval trust regions and all-or-nothing outcomes in the binary-action case. For richer state spaces, the misaligned adviser optimally selects boundary messages to maximize distance from the truth, yielding potentially non-convex TRS geometries and ball-shaped regions in symmetric settings. The results provide concrete design implications for AI deployment, offering guardrail-based decision protocols and a principled certification method via saddle-point constructions, with future work focused on broader comparative statics and computable trust-region determination. Overall, the work delivers a principled, minimax-based blueprint for safely leveraging AI advice in high-stakes environments while clarifying when and how trust in advice should be bounded.

Abstract

An agent chooses an action using her private information combined with recommendations from an informed but potentially misaligned adviser. With a known alignment probability, the adviser reports his signal truthfully; with remaining probability, the adviser can send an arbitrary message. We characterize the decision rule that maximizes the agent's worst-case expected payoff. Every optimal rule admits a trust region representation in belief space: advice is taken at face value when it induces a posterior within the trust region; otherwise, the agent acts as if the posterior were on the trust region's boundary. We derive thresholds on the alignment probability above which the adviser's presence strictly benefits the agent and fully characterize the solution in binary-state as well as binary-action environments.
Paper Structure (27 sections, 19 theorems, 88 equations)

This paper contains 27 sections, 19 theorems, 88 equations.

Table of Contents

  1. Introduction
  2. Literature review
  3. Model
  4. Main Results
  5. Trust Region Strategies
  6. Optimality of Trust Region Strategies
  7. Robust Rationalizability
  8. Minimal Viable Alignment
  9. Binary State
  10. Multiple States
  11. Binary Action
  12. Rich Private Strategies
  13. Concluding Remarks
  14. Summary.
  15. Implications for AI use.
  16. ...and 12 more sections

Key Result

Theorem 1

Any optimal strategy $\sigma^*$ is equivalent to a trust region strategy with a connected trust region $T$.

Theorems & Definitions (39)

  • Definition 1
  • Theorem 1: Trust Region Solution
  • proof
  • Corollary 1
  • Definition 2: Robustly Rationalizable Strategy
  • Theorem 2: Robustly Rationalizable Solution
  • proof
  • Definition 3: Minimal Viable Alignment
  • Theorem 3: Minimal Viable Alignment
  • proof
  • ...and 29 more