Multi-Objective Reinforcement Learning with Scale-Invariant Q-Functions
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Solution Overview
Problem
Reinforcement learning systems struggle to effectively balance multiple, potentially conflicting objectives due to issues with determining optimal weights and scale variance in reward values, leading to dominance by objectives with larger rewards and requiring trial-and-error adjustments.
Innovation Solution
The method involves determining separate action-value functions for each objective, combining them in distribution space with constraints to maintain scale invariance, using temperature parameters and KL divergence to adjust objective contributions, and employing a two-step policy update process.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If separate action-value functions are determined for each objective, then objectives are weighted independently of reward scales (scale invariance), but the system complexity increases due to multiple functions and combination mechanisms
Solution Approach 1:
The patent divides the single action-value function into multiple separate action-value functions, each dedicated to a specific objective. This segmentation allows each function to independently evaluate its corresponding objective without being influenced by the scale of other objectives' rewards, thereby achieving scale invarance and more stable learning across multiple objectives.
Solution Approach 2:
The patent introduces temperature parameters as intermediary elements that mediate the combination of multiple action-value functions. These temperature parameters control the influence of each objective during the combination process, enabling flexible balancing of competing objectives while maintaining scale invarance. The intermediary mechanism transforms the complex multi-objective problem into a manageable combination of scaled individual objectives.
2Adaptability or versatility
If objectives are combined in reward space with weight transformation, then the system can handle multiple objectives, but objectives with larger rewards dominate the learning process
Solution Approach 1:
The patent transitions from combining objectives in reward space (scalar dimension) to combining them in distribution space (probability distribution dimension). By determining separate action-value functions for each objective and combining their distributions rather than their scalar rewards, the system maintains adaptability to handle multiple objectives while preventing dominance by objectives with larger reward scales. This dimensional transformation preserves the relative importance of each objective independently of reward magnitudes.
3Reliability
If trial-and-error adjustments are used to balance objectives, then optimal weights can be found, but the training process requires extensive time and computational resources
Solution Approach 1:
The patent introduces temperature parameters as adjustable controls that directly influence the combination of action-value functions. Instead of requiring extensive trial-and-error adjustments of weight parameters, the temperature parameters provide a more direct and efficient mechanism for balancing objectives. By changing the temperature parameters, the system can quickly adapt the relative influence of different objectives without the extensive iterative weight tuning that characterizes traditional approaches.
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AI summary
There is provided a method for training a neural network system by reinforcement learning, the neural network system being configured to receive an input observation characterizing a state of an environment interacted with by an agent and to select and output an action in accordance with a policy that aims to satisfy a plurality of objectives. The method comprises obtaining a set of one or more trajectories. Each trajectory comprises a state of an environment, an action applied by the agent to the environment according to a previous policy in response to the state, and a set of rewards for the action, each reward relating to a corresponding objective of the plurality of objectives. The method further comprises determining an action-value function for each of the plurality of objectives based on the set of one or more trajectories. Each action-value function determines an action value representing an estimated return according to the corresponding objective that would result from the agent performing a given action in response to a given state according to the previous policy. The method further comprises determining an updated policy based on a combination of the action-value functions for the plurality of objectives.