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Persuasive Prediction via Decision Calibration

NeurIPS 2026 · Learning theory and algorithms › Prediction and decision losses · approach: Probabilistic calibration · 0 citations (OpenAlex)

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Proposes persuasive prediction, where a sender without a known prior learns a decision-calibrated randomized predictor from finite data via a minimax/no-regret algorithm (PerDecCal) that matches the restricted Bayesian persuasion benchmark.

Problem

Bayesian persuasion assumes a common prior, which is infeasible to learn in high-dimensional or infinite state spaces; the paper asks how receivers should be modeled without a common prior and whether a sender with finite data can match a fully informed Bayesian sender.

Approach

Replace the common-prior assumption with decision calibration (predictions unbiased conditioned on each receiver's best response), which guarantees no swap regret; learn an optimal decision-calibrated randomized predictor by casting it as a zero-sum game between predictor and Lagrange multipliers solved with best-response vs no-regret dynamics and an ERM oracle.

Key results

• PerDecCal with n >= O(log(|H|Ndm/delta)/eps^4) samples outputs a predictor whose sender utility is within eps of the best in-class decision-calibrated predictor, with DecCE at most gamma+eps.
• In the single-receiver case, the algorithm matches the utility of a fully informed Bayesian sender restricted to the same predictor class (BayesOPT minus eps).
• Decision-calibrated predictors give receivers swap regret at most 2L|A| eps, and smoothed versions extend guarantees to quantal-response receivers with an extra (ln m+1)/eta term.

Surprising findings

• Strict best response makes sender utility discontinuous: two eps-decision-calibrated predictors close in sup norm can give sender utilities 1 and 0, motivating quantal response smoothing.

Limitations

• Requires finite hypothesis class for the main algorithm; infinite-class case needs quantal response smoothing and covering number bounds.
• Relies on receivers best responding to (approximately) decision-calibrated predictions, a behavioral assumption.
• Strict best response is discontinuous, so uniform estimation of sender utility fails without smoothing.

Experimental setup

Metrics: sender utility decision calibration error swap regret

Baselines: Bayesian persuasion with known prior online calibration-based persuasion

Builds on: Bayesian persuasion decision calibration calibration and Bayesian persuasion (online) quantal response

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