Certified Corruption Budgets: Anytime-Valid Leaderboard Claims under Adaptive Rigging

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Comprehensive Research Summary: Certified Corruption Budgets

This research introduces a novel framework for providing robust guarantees on public leaderboards for AI models against sophisticated, adaptive attackers who continuously monitor published rankings. The central innovation is the Certified Corruption Budget (B bt), a quantifiable measure of corruption tolerance that allows claims about model performance (such as lead or edge) to remain valid even when records are forged or altered in bursts by an attacker.

Core Problem Addressed

Existing guarantees for leaderboards are insufficient because they typically assume either genuine data or bound the corruption per single step. Adaptive attackers—who can observe every published standing, engage in vote rigging, selectively disclose private variants, and exploit benchmark contamination—can evade these static or per-step bounds by corrupting records in unpredictable bursts. The authors address this by developing a tolerance that is robust against such dynamic corruption patterns.

The Certified Corruption Budget (B bt)

The B bt is the key mechanism. It is a corruption tolerance computed after t records have been processed for a specific pairwise claim and published alongside that claim. The fundamental guarantee provided by this budget is:

With probability at least 1 - alpha, simultaneously at all times, the claim (e.g., Model A leads Model B) is correct or more than B bt records have been corrupted or altered.

This formulation ensures that if the claim appears to be true, it is either truly true or the corruption level exceeds a quantifiable threshold (B bt).

Dual Certificates and Claim Types

The framework provides two distinct certificates based on the type of claim being made:

1. The Lead Claim: Guarantees that one model leads another on average up to that point in time.

2. The Edge Claim: Guarantees that one model has held an advantage over another at some specific point in time, which is relevant when the lead claim's win chances are stable.

Computational Mechanism and Cost Analysis

The tolerance B bt is computed by employing a betting strategy based on the claim itself. This strategy involves:

• Evidence Weighting: Betting on the claim based on evidence won beyond what genuine records alone would require.

• Cost per Record: Dividing this evidence by a defined cost per record, which represents the minimum amount of corruption required to fake a single vote.

The construction is rigorously analyzed through four key properties:

1. Direct Counting: The tolerance B bt directly counts corrupted records.

2. Distinguishing Forgery vs. Alteration: It differentiates between forging a new vote and altering a previously seen one; the cost structure is designed such that roughly doubling the cost per record restores the guarantee against altered votes.

3. Optimality in i.i.d. Settings: For independent and identically distributed (i.i.d.) records without ties, this method achieves a tolerance growth rate that is nearly as fast as any valid method can reach, demonstrating near-optimality under ideal conditions (rho:= k g(lambda) + c(lambda)).

4. Efficient Publishing: The cost associated with publishing the best of V private variants grows only logarithmically (V), ensuring low overhead for reporting multiple models.

Robustness Against Adaptive Attackers

The paper rigorously defines and analyzes three classes of adaptive attackers:

• Predictable Attackers (P): Attackers whose corruption pattern is known or predictable. The insertion cost is shown to be valid against this class.

• Value-Dependent Attackers (V): Attackers whose strategy depends on the actual outcomes observed so far. The replacement cost is required to guarantee validity against this class.

• Offline Attackers (O): Attackers who see all uncorrupted values before acting (the strongest class). The replacement cost, when charged roughly twice as much per record, is proven to be valid even against this class under the null hypothesis of O.

Crucially, the paper demonstrates that no existing method covers this entire setting, and it provides a procedure that requires no bound on the number of corrupted records.

Key Theoretical Insights and Results

• Certificate Robustness: The certificate for forged records fails against an attacker who flips votes they have already seen. The certificate for altered records requires roughly twice the charge per record to remain valid.

• Growth Rate Convergence: The certified budget's growth rate approaches the theoretical optimum (rho), meaning it scales nearly as fast as any theoretically possible tolerance method.

• Simultaneous Claims: A second certificate is introduced to cover the lead claim, and its cost is shown to be comparable to the primary lead claim certificate, achieving optimal rates.

• Closed Testing: The framework allows for certifying joint claims (e.g., simultaneous leads) with a price related to the number of pairs being tested.

Empirical Validation

The theoretical guarantees are strongly supported by empirical evidence:

• Chatbot Arena: Results from replays on 1.8 million votes show that a few hundred rigged votes invalidate standard confidence intervals, whereas the certified budget remains valid. On real votes, the certificate proves that clearly separated models can withstand approximately 2,000 forged votes.

• Benchmarks (HELM/SWE-bench): The results are confirmed on static benchmarks like HELM and SWE-bench Verified runs. For instance, on HELM benchmarks, a significant number of ordered pairs are certified pair-by-pair or simultaneously by closed testing. The largest simultaneous tolerance among the top five models is demonstrated to be relatively small (e.g., 17 forged or 7 contaminated items), suggesting the system's limitations under high corruption scenarios.

• Real Data Consistency: The final tolerance does not depend on the order of records, being identical over 100 random permutations for every pair, lending strong confidence in its independence from specific ordering assumptions.

Conclusion

The paper successfully introduces a mathematically rigorous and practically applicable method—the Certified Corruption Budget—to establish provable robustness for AI model leaderboards against adaptive adversaries. By moving beyond per-step bounds to a tolerance that accounts for burst corruption and different attacker classes (P, V, O), the authors provide a new standard for ensuring the integrity of publicly reported AI performance metrics. The combination of theoretical optimality, cost efficiency (V), and validation on large-scale real data positions this work as a significant advancement in robust statistical inference for machine learning leaderboards.

1. Identify Adaptive Corruption Budget for Claims: Implement a mechanism to compute a certified corruption budget, a tolerance Bbt computed after t records and published with each pairwise claim, which ensures With probability at least 1 − α, simultaneously at all times, the claim is correct or more than Bbt records were corrupted.

2. Distinguish Forgeries from Alterations: Develop distinct certificates for different types of corruption to maintain robustness against specific attacks, as the paper states: the certificate for forgeries fails against altered votes. Roughly doubling the cost per record restores the guarantee.

3. Certify Leader Claim Dynamically: Establish a certification process that guarantees validity even while continuously reading data, ensuring that The guarantee is anytime-valid, which holds at all times simultaneously.

4. Price Model Selection Robustly: When publishing the best of many private variants, use a cost structure derived from Publishing the best of V private variants costs only an amount growing like log V, to ensure selection rules do not lead to false statements, as suggested by Selection costs between log V − log(2M+) and log V nats.

5. Handle Simultaneous Leader Claims: For complex scenarios involving multiple claims, use a method that allows for joint certification of all claims simultaneously, as demonstrated by the Simultaneous certificates which show that The set S∗ of true nulls in Proposition 5.6 is fixed, while the pairs with ∆ijt ≤ 0 change with t.