Zero-Suppressed Decision Diagram for Fitted Q-Iteration
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Solution Overview
Problem
Fitted Q-iteration algorithms face challenges in handling large or continuous state and action spaces, making it difficult to determine optimal control policies efficiently, especially in applications like computational material discovery where massive computation and experimentation are required.
Innovation Solution
The implementation of a zero-suppressed decision diagram (ZDD) in Fitted Q-iteration, which allows for faster updates of state-action value functions by using sparse bit vectors and compact data structures, enabling efficient computation even in large action spaces.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If tabular form is used to represent the Q-function for finite state and action spaces, then the approximation and control policy are straightforward, but the approach cannot be used successfully when dealing with continuous or very large discrete state and/or action spaces
Solution Approach 1:
The patent transforms the Q-function representation from tabular form to a parametric form Q(s, a; w, θ), where the function is defined by parameters w and θ rather than explicit table entries. This allows the same parametric representation to handle both discrete and continuous state-action spaces by changing the parameterization approach, thus resolving the contradiction between ease of operation for small spaces and adaptability for large/continuous spaces.
2Reliability
If Fitted Q-iteration is applied to large action spaces, then optimal control policies can be determined, but the computational time and resources increase significantly
Solution Approach 1:
The patent replaces the traditional iterative updating mechanism of Fitted Q-iteration with a gradient-based optimization approach. Instead of repeatedly updating Q-values through iteration, the method uses gradient descent to directly optimize the parameters w and θ, substituting the mechanical iterative process with a more efficient mathematical optimization approach that reduces computational time while maintaining reliability in determining optimal policies.
Solution Approach 2:
The patent changes the optimization approach from value iteration to gradient-based parameter optimization. By formulating the problem as minimizing a loss function with respect to parameters w and θ, and using gradient descent to update these parameters, the method achieves faster convergence compared to traditional Fitted Q-iteration, thus reducing computational time while maintaining the ability to determine optimal control policies.
Data Source
AI summary
A computer-implemented method for estimating a state-action value function for a Fitted Q-iteration is provided including obtaining a set of tuples D and a discount factor γ, each of the set of tuples including a state s, an action a, a reward r, and a resulting state s′, constructing a zero-suppressed decision diagram (ZDD) of feature vectors {ϕ(s′, a′)|a′∈(s′)} for each of the resulting states s′ of the set of tuples, where the feature vector ϕ(s, a) is a sparse bit vector {0,1}D and (s′) is the set of actions applicable at state s′, updating parameters w∈D, θ of a state-action value function Q (s, a; w, θ); and repeating the updating step a predetermined times by incrementing t.