Tensor-Efficient High-Dimensional Q-learning

High-dimensional reinforcement learning faces challenges with complex calculations and low sample efficiency in large state-action spaces. Q-learning algorithms struggle particularly with the curse of dimensionality, where the number of state-action pairs grows exponentially with problem size. While neural network-based approaches like Deep Q-Networks have shown success, recent tensor-based methods using low-rank decomposition offer more parameter-efficient alternatives. Building upon existing tensor-based methods, we propose Tensor-Efficient Q-Learning (TEQL), which enhances low-rank tensor decomposition via improved block coordinate descent on discretized state-action spaces, incorporating novel exploration and regularization mechanisms. The key innovation is an exploration strategy that combines approximation error with visit count-based upper confidence bound to prioritize actions with high uncertainty, avoiding wasteful random exploration. Additionally, we incorporate a frequency-based penalty term in the objective function to encourage exploration of less-visited state-action pairs and reduce overfitting to frequently visited regions. Empirical results on classic control tasks demonstrate that TEQL outperforms conventional matrix-based methods and deep RL approaches in both sample efficiency and total rewards, making it suitable for resource-constrained applications, such as space and healthcare where sampling costs are high.