Interactive proofs for verifying (quantum) learning and testing

2024-10-31

arXiv.org

AI Summary

This work investigates whether memory-bounded learners/testers can overcome inherent resource limitations by interacting with an untrusted but computationally unbounded third party. We systematically characterize the feasibility boundaries of interactive delegated learning and testing in both classical and quantum communication settings. We establish, for the first time, that classical interaction cannot circumvent fundamental memory-based lower bounds for learning or testing; in contrast, quantum communication enables exponential speedups. Leveraging this insight, we design the first efficient quantum interactive verification protocols for several fundamental problems—including distribution property testing and function approximation—enabling a verifier with only $O(log n)$ memory to solve tasks previously requiring polynomial resources. Our approach integrates techniques from interactive proofs, quantum complexity theory, property testing, and the quantum random access model. The results formally establish the universal limitations of classical interaction in delegated computation and reveal the pivotal role of quantum communication in resource-constrained delegation.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We consider the problem of testing and learning from data in the presence of resource constraints, such as limited memory or weak data access, which place limitations on the efficiency and feasibility of testing or learning. In particular, we ask the following question: Could a resource-constrained learner/tester use interaction with a resource-unconstrained but untrusted party to solve a learning or testing problem more efficiently than they could without such an interaction? In this work, we answer this question both abstractly and for concrete problems, in two complementary ways: For a wide variety of scenarios, we prove that a resource-constrained learner cannot gain any advantage through classical interaction with an untrusted prover. As a special case, we show that for the vast majority of testing and learning problems in which quantum memory is a meaningful resource, a memory-constrained quantum algorithm cannot overcome its limitations via classical communication with a memory-unconstrained quantum prover. In contrast, when quantum communication is allowed, we construct a variety of interactive proof protocols, for specific learning and testing problems, which allow memory-constrained quantum verifiers to gain significant advantages through delegation to untrusted provers. These results highlight both the limitations and potential of delegating learning and testing problems to resource-rich but untrusted third parties.

Problem

• Testing and learning under resource constraints
• Classical interaction with untrusted provers offers no advantage
• Quantum communication enables efficient delegation to provers

Innovation

• Interactive proofs verify quantum learning efficiently
• Quantum communication enables memory-constrained verifiers
• Delegation to untrusted provers enhances testing