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Safely Learning Optimal Auctions: A Testable Learning Framework for Mechanism Design
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Proposes a regularized testable learning framework for mechanism design that tests whether value distributions are close to regular, yielding a tester-learner pair for revenue-optimal auctions and testers for Bulow-Klemperer and anonymous price auctions.
Problem
Distributional assumptions such as regularity of bidder value distributions underpin many auction theory results, but regularity cannot be tested within the original testable learning framework, so it is unclear when these results can be trusted on a given dataset.
Approach
Relaxes the testable learning soundness guarantee so the learner must compete with the optimal mechanism of any regular distribution KS-close to the input, rather than the input's own optimum; a quantile-shifted empirical distribution tester checks whether a close regular distribution exists.
Key results
- Shows the original testable learning framework cannot yield nontrivial revenue guarantees: no m-sample conventional tester exists for revenue-optimal learning (Theorem 3).
- Regularized tester-learner pair achieves revenue at least (1 - O(sqrt(n alpha))) OPT of any close regular distribution with m = O~(log(1/delta)/alpha^2) samples (Theorem 6).
- Lower bound: for any mechanism there is an irregular distribution where revenue is at most (1 - Omega(sqrt(alpha))) OPT of a close regular distribution (Lemma 11).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use regularized testable learning with the proposed tester and learner | Single-item revenue-optimal auctions · Product distributions close to regular distributions | revenue ratio to OPT(D′): (1 − O(√nα)) | Helped |
| Use the tester to certify the Bulow-Klemperer guarantee | Vickrey auction with one additional bidder · i.i.d. bidders, with D′ regular and α-close to D | revenue ratio to OPTn(D′): (1 − O(√nα)) | Helped |
| Use the tester to certify an anonymous reserve price | Anonymous price auction · Independent bidders, with each D′i regular and α-close to Di | revenue ratio to OPT(D′): 1/e (1 − O(√nα)) | Helped |
| Replace conventional testable learning with regularized testable learning | Revenue-optimal auction learning · Irregular distributions | existence of a nontrivial tester-learner guarantee | Helped |
Surprising findings
- Testing regularity directly is impossible within the original testable learning framework, since revenue ratios can blow up for distributions indistinguishable from regular ones.
- Regular distributions are not dense in KS distance: some irregular distribution is bounded away from every regular distribution.
Limitations
- Results are theoretical with no empirical evaluation.
- Assumes product distributions and, for Bulow-Klemperer, i.i.d. bidders; the tester does not check these assumptions.
- Multi-bidder lower bound remains open.
Experimental setup
Metrics: revenue approximation ratio sample complexity
Baselines: conventional testable learning framework
Builds on: testable learning (Rubinfeld & Vasilyan, 2023) Guo et al. 2019 sample complexity of optimal auctions Guo et al. 2021 link function learning Devanur et al. 2016 revenue monotonicity Hartline & Roughgarden 2009 anonymous pricing
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