A Generalized Algorithm for Multi-Objective Reinforcement Learning and Policy Adaptation (1908.08342v2)

Abstract: We introduce a new algorithm for multi-objective reinforcement learning (MORL) with linear preferences, with the goal of enabling few-shot adaptation to new tasks. In MORL, the aim is to learn policies over multiple competing objectives whose relative importance (preferences) is unknown to the agent. While this alleviates dependence on scalar reward design, the expected return of a policy can change significantly with varying preferences, making it challenging to learn a single model to produce optimal policies under different preference conditions. We propose a generalized version of the BeLLMan equation to learn a single parametric representation for optimal policies over the space of all possible preferences. After an initial learning phase, our agent can execute the optimal policy under any given preference, or automatically infer an underlying preference with very few samples. Experiments across four different domains demonstrate the effectiveness of our approach.

• The paper presents an envelope Q-learning algorithm that leverages a generalized Bellman equation to optimize policies across varied, unknown preferences.
• The paper provides theoretical convergence guarantees and demonstrates scalable neural network implementations validated on multiple domains.
• The paper employs techniques like Hindsight Experience Replay and homotopy optimization to enhance sample efficiency and policy adaptability.

A Generalized Algorithm for Multi-Objective Reinforcement Learning and Policy Adaptation

The paper explores a novel algorithmic approach within the field of Multi-Objective Reinforcement Learning (MORL), aiming to enhance policy learning and adaptation under multiple unknown preferences. MORL focuses on learning policies that optimize several competing objectives without predefined scalarization of rewards. This is crucial in scenarios where agent tasks cannot be effectively reduced to a single scalar reward due to dynamic or unknown preference weights.

Overview

The paper introduces an algorithm leveraging a generalized BeLLMan equation, which facilitates learning a unified parametric representation for optimal policies across a spectrum of preferences. This representation enables the agent to infer underlying preferences with few samples and execute the optimal policy tailored to any specified preference vector. Essentially, this approach contrasts with traditional single-objective RL methods by accommodating a broader and more adaptable policy learning framework.

The proposed method efficiently navigates the complexities of learning policies in varying MORL contexts by solving the convex coverage set (CCS) of the Pareto frontier. The CCS includes all potential returns maximizing utility for any linear preference function. The framework focuses on two central contributions:

1. Convergence Analysis: Providing theoretical guarantees for multi-objective Q-Learning’s convergence using envelope Q-learning. This is achieved by showing that the envelope optimality operator is a contraction and that its fixed point corresponds to the preferred optimal value function within the preference space.
2. Scalable Neural Network Implementation: Demonstrating that deep neural networks can effectively scale MORL to larger domains. The architecture facilitates learning by using a single network to represent policies across diverse preferences, optimizing for the convex envelope of Q-values.

Methodology

The authors developed an envelope Q-learning algorithm, which operates within a specifically defined value space using vectorized Q-functions. The optimality operator, constructed as a contraction, ensures convergence to a Pareto-optimal solution. To handle practical implementation challenges, the paper employs:

• Hindsight Experience Replay (HER): This mechanism enhances sample efficiency by allowing past transitions to be re-used for different sampled preferences.
• Homotopy Optimization: Adjusts the learning focus progressively, facilitating convergence to a global minimum by interpolating between easy-to-optimize and target loss functions.

Empirical Evaluation

Experiments conducted across four distinct domains—Deep Sea Treasure (DST), Fruit Tree Navigation (FTN), Task-Oriented Dialog, and SuperMario Game—validate the strategy's effectiveness. The agent's performance is measured via Coverage Ratio (CR) and Adaptation Error (AE), indicating the ability to retrieve optimum solutions and adapt policies to test-time preferences.

The empirical results substantiate that the envelope Q-learning algorithm consistently surpasses baseline algorithms, including traditional scalarized approaches in both learning phases and adaptation quality. Especially noticeable is the enhanced policy alignment efficiency with varying user preferences compared to scalarized methods.

Implications and Future Work

In terms of theoretical implications, the ability to maintain a versatile policy across unknown preferences, while upholding the generalizability in high-dimensional spaces, marks notable progress in MORL. Practically, this signifies a significant reduction in the labor-intensive process of reward function design, therefore opening new application avenues in dynamic environments like personal assistants, gaming AI, and adaptive dialog systems.

Future developments could refine the theoretical underpinnings of the multi-objective Banach Fixed-Point theorem and explore extending the model to accommodate non-linear preference functions. Further work may also investigate integrating this approach within broader AI systems, leveraging its adaptability for enhanced decision-making processes in varied complex domains.