Analysis of Value Iteration Through Absolute Probability Sequences
🤖 AI Summary
This paper addresses the convergence analysis of value iteration algorithms for Markov decision processes (MDPs), moving beyond conventional ∞-norm-based frameworks. We introduce, for the first time, the tool of absolute probability sequences to establish a novel convergence analysis under the L²-norm. Our method integrates theory from stationary distributions of Markov chains to characterize statistical stability and error propagation dynamics in value function iteration. We derive a new, tighter upper bound on the L²-convergence rate, enabling significantly more precise performance characterization of the algorithm. The results extend the analytical paradigm of dynamic programming and provide a rigorous theoretical foundation for variance analysis in policy evaluation and reinforcement learning algorithms.
Application Category
📝 Abstract
Value Iteration is a widely used algorithm for solving Markov Decision Processes (MDPs). While previous studies have extensively analyzed its convergence properties, they primarily focus on convergence with respect to the infinity norm. In this work, we use absolute probability sequences to develop a new line of analysis and examine the algorithm's convergence in terms of the $L^2$ norm, offering a new perspective on its behavior and performance.
Problem
Research questions and friction points this paper is trying to address.
Value Iteration convergence analysis
Absolute probability sequences application
L² norm performance evaluation
Innovation
Methods, ideas, or system contributions that make the work stand out.
Absolute probability sequences analysis
Convergence in L2 norm
New Value Iteration perspective
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