Typed Component Algebras for Simulated Annealing and Markov-Chain Monte Carlo

2023-02-06 · Source: cs.SE updates on arXiv.org · Field: Technology & Digital — Software Development & Engineering, Artificial Intelligence & Machine Learning · Depth: Expert, quick

Summary

A new approach, "Typed Component Algebras," refactors Simulated Annealing (SA) and Markov-Chain Monte Carlo (MCMC) algorithms by decomposing their shared Metropolis-Hastings kernel into a typed algebra of five components: objective, cooling schedule, neighborhood, move kernel, and acceptance rule. This modular design, implemented in the open-source Rust-and-Python package anneal, allows improvements like surrogate proposals or noise-aware acceptance rules to be applied universally across classical, fast, generalized, Hamiltonian, or parallel-tempered drivers. The framework ensures correctness through SymPy-checked reductions, which notably surfaced a three-decade-old sign error in visiting-distribution literature, and TLA+ model-checking for safety and liveness properties. A three-channel finite-precision audit also confirmed float16 cannot reproduce float64 basin selection. On the CUTEst collection, anneal outperforms a budget-matched CMA-ES restart heuristic in finding optimal basins, while providing almost-sure convergence and regret guarantees.

Key takeaway

For Machine Learning Engineers or Research Scientists developing optimization algorithms, adopting a typed component algebra approach for SA/MCMC can significantly streamline development. You can implement new algorithmic improvements once, making them universally available across diverse drivers, reducing rewrite and re-verification efforts. This modularity also facilitates formal verification, enhancing algorithm robustness and correctness, as shown by the anneal package's performance and error detection.

Key insights

Decomposing SA/MCMC into a typed component algebra enables modular improvements and verifiable correctness.

Principles

• Modularizing algorithms improves reusability and verification.
• Formal verification can uncover long-standing errors.
• Finite-precision audits are crucial for numerical stability.

Method

The method involves defining SA/MCMC as a typed algebra of five components (objective, cooling schedule, neighborhood, move kernel, acceptance rule) with four local composition laws, allowing a single Sampler step to run any point.

In practice

• Implement new SA/MCMC components once for broad applicability.
• Use SymPy for algebraic reduction verification.
• Apply TLA+ for safety and liveness property checks.

Topics

• Simulated Annealing
• Markov-Chain Monte Carlo
• Component Algebra
• Formal Verification
• Optimization Algorithms
• Rust-and-Python

Best for: AI Scientist, Research Scientist, Machine Learning Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.SE updates on arXiv.org.