Model-based policy gradient (MBPG) has been employed to seek an approximate solution to the optimal control problem. However, there is coupling between adjacent states due to temporal dependencies, making the training time grow linearly with the time horizon. This paper reshapes the training process of MBPG with the time-splitting technique to establish a time-independent algorithm called Training Through Time-Splitting (T3S). First, copy the coupled variables to obtain two independent variables. Meanwhile, an extra variable together with an equivalence constraint is introduced for problem consistency. Then, the transformed problem divides into subproblems with carefully derived loss functions. Subproblems own decoupled variables and shared policy networks, which means they can be optimized concurrently. Guided by the algorithm design, this paper further proposes an asynchronous parallel training scheme to accelerate training efficiency. Numerical simulation shows that the T3S algorithm outperforms the MBPG algorithm by 83.6% in wall-clock time with a trajectory tracking task.

Cover Caption: The cover image is based on the Research Article Direct and indirect reinforcement learning by Yang Guan et al., https://doi.org/10.1002/int.22466.

Reinforcement learning (RL) algorithms have been successfully applied to a range of challenging sequential decision-making and control tasks. In this paper, we classify RL into direct and indirect RL according to how they seek the optimal policy of the Markov decision process problem. The former solves the optimal policy by directly maximizing an objective function using gradient descent methods, in which the objective function is usually the expectation of accumulative future rewards. The latter indirectly finds the optimal policy by solving the Bellman equation, which is the sufficient and necessary condition from Bellman's principle of optimality. We study policy gradient (PG) forms of direct and indirect RL and show that both of them can derive the actor–critic architecture and can be unified into a PG with the approximate value function and the stationary state distribution, revealing the equivalence of direct and indirect RL. We employ a Gridworld task to verify the influence of different forms of PG, suggesting their differences and relationships experimentally. Finally, we classify current mainstream RL algorithms using the direct and indirect taxonomy, together with other ones, including value-based and policy-based, model-based and model-free.

Hashing-based cross-modal search which aims to map multiple modality features into binary codes has attracted increasingly attention due to its storage and search efficiency especially in large-scale database retrieval. Recent unsupervised deep cross-modal hashing methods have shown promising results. However, existing approaches typically suffer from two limitations: (1) They usually learn cross-modal similarity information separately or in a redundant fusion manner, which may fail to capture semantic correlations among instances from different modalities sufficiently and effectively. (2) They seldom consider the sampling and weighting schemes for unsupervised cross-modal hashing, resulting in the lack of satisfactory discriminative ability in hash codes.