Efficient Interactive Proofs for Agnostic Learning of Boolean Functions

Conceptos Básicos

The authors construct efficient interactive proof systems that enable a verifier to check the results of an untrusted learner for various classes of Boolean functions, including heavy Fourier characters, AC0[2] circuits, and k-juntas, while using significantly fewer samples than the learner.

Resumen

The paper presents several results on constructing efficient interactive proof systems for verifying the results of agnostic learning algorithms over the uniform distribution:

1. Learning Heavy Fourier Characters:

• The authors construct an interactive protocol where the verifier uses only poly(t/ε) random examples to learn the t heaviest Fourier characters of a given Boolean function up to an error ε. This improves upon the previous protocol of [GRSY21] whose sample complexity depended on the number of variables n.
• The key ideas are a novel algorithm for approximately computing the highest t Fourier coefficients, and a framework for reducing the number of queries to samples.

2. Learning AC0[2] Circuits:

• The authors show that for any function f such that the distance of f from AC0[2] circuits is non-negligible, the class AC0[2] is (polylog(n), 1/10)-PAC-verifiable over the uniform distribution, where the verifier uses at most quasi-polynomially many random examples.
• This builds on the agnostic learner for AC0[2] from [CIKK17] and a careful analysis of the query patterns in their algorithm.

3. Learning Juntas:

• The authors construct a PAC-verification protocol for the class of k-juntas, where the verifier uses only 2^k · poly(k/ε) random examples, while the honest prover uses k^2^k/ε^2 · log(n) examples.
• This is obtained by a general transformation from tolerant testers to PAC-verifiers, combined with the query-to-sample reduction framework.

4. Unbounded Provers:

• The authors show that if the honest prover is allowed to be computationally unbounded, then any class of Boolean functions can be distribution-free, proper, (ε, 1/10)-PAC-verifiable using only O(1/ε) random examples.
• This is achieved by viewing agnostic learning as an Empirical Risk Minimization task and delegating it to an unbounded prover.

Overall, the paper demonstrates the power of interactive proofs in verifying the results of agnostic learning algorithms, achieving quantitative and qualitative improvements over standalone learners.

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Ideas clave extraídas de

On the Power of Interactive Proofs for Learning

by Tom Gur,Moha... a las arxiv.org 04-15-2024

https://arxiv.org/pdf/2404.08158.pdf

Consultas más profundas

What are some potential applications of the PAC-verification protocols developed in this work, beyond the specific function classes studied

The PAC-verification protocols developed in this work have potential applications beyond the specific function classes studied. One key application is in the field of anomaly detection in various domains such as cybersecurity, fraud detection, and healthcare. By using interactive proofs for verifying the results of anomaly detection algorithms, organizations can ensure the accuracy and reliability of the detection process without compromising sensitive data. Additionally, these protocols can be applied in quality control processes in manufacturing industries to verify the performance of machine learning models used for defect detection and product quality assessment. Furthermore, in financial services, PAC-verification protocols can be utilized to validate the outcomes of predictive models for risk assessment and investment decisions, ensuring compliance with regulatory standards and enhancing transparency in decision-making processes.

Can the query-to-sample reduction framework be extended to handle adaptive queries that may depend on the interaction with the prover

The query-to-sample reduction framework can potentially be extended to handle adaptive queries that depend on the interaction with the prover. By incorporating adaptive query strategies into the framework, the verifiers can dynamically adjust their query patterns based on the responses received from the prover during the interaction. This adaptability can enhance the efficiency and effectiveness of the verification process, allowing the verifiers to optimize their query selection based on the information provided by the prover. Additionally, handling adaptive queries can enable the framework to accommodate more complex scenarios where the queries need to be tailored in real-time based on the evolving context of the interaction.

Are there other learning tasks beyond agnostic learning where interactive proofs could provide significant advantages over standalone learners

Interactive proofs could provide significant advantages over standalone learners in various learning tasks beyond agnostic learning. One such task is reinforcement learning, where interactive proofs can be used to verify the policies learned by reinforcement learning agents in dynamic environments. By incorporating interactive verification mechanisms, organizations can ensure the safety and reliability of autonomous systems powered by reinforcement learning algorithms, mitigating the risks associated with incorrect or unsafe decision-making. Additionally, in online learning scenarios, interactive proofs can be leveraged to validate the continuous learning process and detect any deviations or biases in the learning outcomes, enhancing the overall robustness and fairness of the learning algorithms.