Multi-Objective Reinforcement Learning via Set-Valued Value Function
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Solution Overview
Problem
Current multi-objective reinforcement learning methods struggle to efficiently obtain Pareto-optimal policies in dynamic systems with continuous state spaces and multiple objectives, often requiring extensive computational resources and prior knowledge of transition probabilities, while failing to access the entire Pareto front due to limitations in handling continuous state spaces and linear scalarization methods.
Innovation Solution
A generative neural network is employed to model a set-valued state-action value function, which generates multiple vector outputs by sampling noise vectors from a specified probability distribution, optimizing parameters through a novel loss function that quantifies the set-valued temporal difference error induced by the multi-objective Bellman optimality equation, allowing access to the entire Pareto front without relying on conventional linear scalarization.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If linear scalarization methods are used to solve multi-objective reinforcement learning problems, then the problem can be transformed into single-objective problems, but only the convex part of the Pareto front can be discovered
Solution Approach 1:
The method segments the multi-objective problem by generating multiple scalarized sub-problems with different weight combinations, where each sub-problem focuses on optimizing a specific trade-off between objectives. This segmentation allows systematic exploration of different regions of the Pareto front through coordinated solving of simpler single-objective problems.
Solution Approach 2:
The method dynamically adjusts the weight vectors and explores different regions of the objective space iteratively. By adaptively modifying scalarization parameters and using policy iteration across multiple scalarized problems, the approach dynamically converges to a more complete approximation of the entire Pareto front rather than being static in its exploration.
2Reliability
If stochastic dynamic programming is used with linear scalarization, then the Bellman optimality equation can be solved, but the state space must be discrete and finite
Solution Approach 1:
The method substitutes the traditional stochastic dynamic programming mechanical framework (which requires discrete states and exhaustive enumeration) with a policy iteration approach that works with scalarized objective functions. This substitution enables handling of continuous state spaces by using gradient-based or sampling-based evaluation rather than exhaustive state-space traversal.
Solution Approach 2:
The method changes the parameterization of the value function and policy representation to accommodate continuous state spaces. By using parametric policies and value functions that can operate in continuous domains, the approach maintains the iterative optimization structure while extending applicability beyond discrete state spaces.
3Manufacturing precision
If multiple independent optimizations are performed to approximate the Pareto front densely, then more Pareto-optimal policies can be obtained, but the computational cost increases significantly
Solution Approach 1:
The method merges multiple scalarized optimization problems into a coordinated policy iteration framework. By sharing computational components and iteratively refining policies across multiple scalarized sub-problems rather than solving them completely independently, the approach achieves dense Pareto front approximation with reduced redundant computation.
Solution Approach 2:
The method performs preliminary exploration and initialization that guides subsequent optimizations toward promising regions of the Pareto front. By pre-processing the objective space and initializing policies based on preliminary scalarized solutions, the approach reduces the computational burden of achieving dense approximation compared to performing multiple completely independent optimizations.
4Reliability
If prior knowledge of transition probabilities is required for stochastic dynamic programming, then optimal policies can be found, but such knowledge is limited in realistic use cases
Solution Approach 1:
The method enables the system to learn and estimate transition dynamics from data rather than requiring pre-specified prior knowledge. Through iterative interaction with the environment and data-driven estimation of transition probabilities, the approach makes the system self-sufficient in realistic scenarios where complete prior knowledge is unavailable, while still achieving optimal policies.
Data Source
AI summary
Systems and methods described herein can involve obtaining Pareto optimal solutions through making sequential decisions in a system that has multi-dimensional rewards and a continuous state space, and is controllable through a finite discrete set of actions, involving learning a value function through reinforcement learning (RL), wherein the value function is configured to take in an input of a state and an action pair, and provides a set of vectors as output, each of the set of vectors representing an expected total sum of rewards corresponding to a sequence of future control decisions; receiving, at an initial stage of a control sequence, a request about a total sum of rewards to be achieved; and determining a sequence of actions iteratively based on the output of the value function, an observation of the current state, and the request.