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[2511.19628] Optimization and Regularization Under Arbitrary Objectives
Summary
This article explores the limitations of Markov Chain Monte Carlo (MCMC) methods in optimization and regularization under arbitrary objectives, focusing on likelihood sharpness and its impact on performance in reinforcement learning tasks.
Why It Matters
Understanding the effectiveness of MCMC methods in various optimization scenarios is crucial for researchers and practitioners in machine learning. This study reveals how likelihood sharpness influences model performance, providing insights that could enhance algorithm design and application in complex tasks.
Key Takeaways
- MCMC methods' performance is heavily influenced by the sharpness of the likelihood function.
- Introducing a sharpness parameter can optimize regularization in data-driven approaches.
- Empirical applications demonstrate the relevance of likelihood curvature in reinforcement learning.
- A hybrid approach combining optimization and MCMC can yield competitive results.
- Excessive likelihood sharpness may lead to over-concentration on a single mode, affecting model robustness.
Statistics > Machine Learning arXiv:2511.19628 (stat) [Submitted on 24 Nov 2025 (v1), last revised 15 Feb 2026 (this version, v2)] Title:Optimization and Regularization Under Arbitrary Objectives Authors:Jared N. Lakhani, Etienne Pienaar View a PDF of the paper titled Optimization and Regularization Under Arbitrary Objectives, by Jared N. Lakhani and 1 other authors View PDF Abstract:This study investigates the limitations of applying Markov Chain Monte Carlo (MCMC) methods to arbitrary objective functions, focusing on a two-block MCMC framework which alternates between Metropolis-Hastings and Gibbs sampling. While such approaches are often considered advantageous for enabling data-driven regularization, we show that their performance critically depends on the sharpness of the employed likelihood form. By introducing a sharpness parameter and exploring alternative likelihood formulations proportional to the target objective function, we demonstrate how likelihood curvature governs both in-sample performance and the degree of regularization inferred by the training data. Empirical applications are conducted on reinforcement learning tasks: including a navigation problem and the game of tic-tac-toe. The study concludes with a separate analysis examining the implications of extreme likelihood sharpness on arbitrary objective functions stemming from the classic game of blackjack, where the first block of the two-block MCMC framework is replaced with an iterative optimization s...
