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Policy Learning with Confidence

Victor Chernozhukov, Sokbae Lee, Adam M. Rosen, Liyang Sun

TL;DR

The paper tackles policy selection when welfare estimates are noisy by introducing risk-aware policy learning, which balances estimated welfare $\widehat{V}(\pi)$ against estimation risk $\widehat{s}(\pi)$ along an efficient frontier. The PoLeCe rule selects $\widehat{\pi}_{PoLeCe}$ by maximizing $\widehat{V}(\pi) - \widehat{q}_{1-\alpha,\Pi}\widehat{s}(\pi)$, where $\widehat{q}_{1-\alpha,\Pi}$ is a bootstrap-based quantile that yields a high-probability, one-sided lower bound on welfare, $LV_{1-\alpha}(\pi) = \widehat{V}(\pi) - \widehat{q}_{1-\alpha,\Pi}\widehat{s}(\pi)$. The framework provides regret bounds for risk-aware rules and shows that a data-driven penalty can place the chosen policy on the efficient frontier with reporting guarantees, while enabling computation via second-order cone programs. An empirical MVPF illustration using the Policy Impacts Library demonstrates how PoLeCe diversifies allocations across programs in light of estimation uncertainty, with allocations differing across adult and youth groups. The work situates PoLeCe within P-certified decisions and highlights its practical relevance for transparent, uncertainty-aware budgeting and policy design, while suggesting avenues for extending the approach to ambiguity and partial identification.

Abstract

This paper introduces a rule for policy selection in the presence of estimation uncertainty, explicitly accounting for estimation risk. The rule belongs to the class of risk-aware rules on the efficient decision frontier, characterized as policies offering maximal estimated welfare for a given level of estimation risk. Among this class, the proposed rule is chosen to provide a reporting guarantee, ensuring that the welfare delivered exceeds a threshold with a pre-specified confidence level. We apply this approach to the allocation of a limited budget among social programs using estimates of their marginal value of public funds and associated standard errors.

Policy Learning with Confidence

TL;DR

The paper tackles policy selection when welfare estimates are noisy by introducing risk-aware policy learning, which balances estimated welfare against estimation risk along an efficient frontier. The PoLeCe rule selects by maximizing , where is a bootstrap-based quantile that yields a high-probability, one-sided lower bound on welfare, . The framework provides regret bounds for risk-aware rules and shows that a data-driven penalty can place the chosen policy on the efficient frontier with reporting guarantees, while enabling computation via second-order cone programs. An empirical MVPF illustration using the Policy Impacts Library demonstrates how PoLeCe diversifies allocations across programs in light of estimation uncertainty, with allocations differing across adult and youth groups. The work situates PoLeCe within P-certified decisions and highlights its practical relevance for transparent, uncertainty-aware budgeting and policy design, while suggesting avenues for extending the approach to ambiguity and partial identification.

Abstract

This paper introduces a rule for policy selection in the presence of estimation uncertainty, explicitly accounting for estimation risk. The rule belongs to the class of risk-aware rules on the efficient decision frontier, characterized as policies offering maximal estimated welfare for a given level of estimation risk. Among this class, the proposed rule is chosen to provide a reporting guarantee, ensuring that the welfare delivered exceeds a threshold with a pre-specified confidence level. We apply this approach to the allocation of a limited budget among social programs using estimates of their marginal value of public funds and associated standard errors.

Paper Structure

This paper contains 23 sections, 7 theorems, 92 equations, 3 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Risk-Aware Policy Choices
  3. Motivation and Risk-Aware Policy Choice
  4. Regret Properties and Guarantees of Risk-Aware Policies
  5. The PoLeCe Rule
  6. Reporting Guarantees
  7. Discussion and Related Literature
  8. Empirical Examples of Investment Allocations for Public Programs
  9. Conclusion
  10. Proofs
  11. Gaussian Bootstrap for Investment Allocation Problem
  12. Exhibits
  13. Details for Gaussian Bootstrap Implementation
  14. Alternative Motivations for Risk-Aware Decisions
  15. Proofs of Propositions \ref{['prop:DM1']} and \ref{['prop:DM2']}
  16. ...and 8 more sections

Key Result

Proposition 1

Under condition eq:gaussian approx, the regret of any RW policy rule $\widehat{\pi}_{\text{RW}}(\widehat{k})$ is bounded with probability at least $1 - 2\beta - 2r_n$ as: In particular, if $0 \le \widehat{k} \lesssim q_{1-\beta,\Pi}$, then with the same probability, Moreover, if $q_{1-\beta,\Pi} \le \widehat{k} \lesssim q_{1-\beta,\Pi}$, then with the same probability,

Figures (3)

  • Figure 1: Efficient Decision Frontier.
  • Figure 2: Welfare estimates against precision
  • Figure 3: Welfare estimates against precision

Theorems & Definitions (9)

  • Proposition 1: Regret Bounds for Risk-Aware Decisions
  • Proposition 2: LCB Guarantees for RW Decisions
  • Remark 1: PoLeCe as Minimizer of the UCB on Regret
  • Proposition 3: Reporting Guarantees and Regret Bounds for PoLeCe
  • Lemma 1: Quantile Comparison
  • Lemma 2: Existence, Uniqueness, and Differentiability of the Root
  • proof : Proof of Lemma \ref{['sec:lem conic']}
  • Proposition 4: Posterior Expected Utility Maximization
  • Proposition 5: Best Posterior Regret-Risk Aware Decision