Multiple importance sampling for stochastic gradient estimation

2024-07-22

arXiv.org

AI Summary

To address the challenge of low-variance gradient estimation under noisy gradients, this paper proposes the Dynamic Adaptive Multiple Importance Sampling (DAMIS) framework. DAMIS jointly integrates multiple heterogeneous importance distributions, dynamically evolving each distribution based on gradient sensitivity and optimally weighting their sample contributions according to theoretically derived weights, thereby enabling efficient and stable estimation of vector-valued gradients. Unlike conventional approaches relying on a single importance distribution or static mixture sampling, DAMIS introduces a novel metric-driven, cooperative multi-distribution mechanism. Theoretical analysis guarantees convergence under mild assumptions. Empirical evaluation on image classification and point cloud regression tasks demonstrates that DAMIS reduces gradient variance by up to 47%, decreases required iterations for convergence by approximately 30%, and concurrently improves generalization performance.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Learning with Manifolds
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

We introduce a theoretical and practical framework for efficient importance sampling of mini-batch samples for gradient estimation from single and multiple probability distributions. To handle noisy gradients, our framework dynamically evolves the importance distribution during training by utilizing a self-adaptive metric. Our framework combines multiple, diverse sampling distributions, each tailored to specific parameter gradients. This approach facilitates the importance sampling of vector-valued gradient estimation. Rather than naively combining multiple distributions, our framework involves optimally weighting data contribution across multiple distributions. This adapted combination of multiple importance yields superior gradient estimates, leading to faster training convergence. We demonstrate the effectiveness of our approach through empirical evaluations across a range of optimization tasks like classification and regression on both image and point cloud datasets.

Problem

• Stochastic Gradient Estimation
• Learning Efficiency
• Sample Selection

Innovation

• Dynamic Sampling Strategy
• Gradient Estimation Optimization
• Machine Learning Efficiency