Deep Reinforcement Learning (DRL) is far from well understood, although its great potential has been demonstrated with a lot of achievements in different practical problems [Badia et al., 2020, Shah et al., 2022, Fawzi et al., 2022, Degrave et al., 2022, OpenAI, 2022]. Consistent efforts are made to gain a better understanding of the learning dynamics of RL agents.

While ridge regression provides shrinkage for the regression coefficients, manyofthecoefficients remain smallbutnon-zero. Performing ridgeregression with the matrix sketch returned by our algorithm and a particular regularization parameter forces coefficients to zero and has a provable(1+) bound on the statisticalrisk.

Distributional reinforcement learning (DRL) estimates the distribution over future returns instead of the mean to more efficiently capture the intrinsic uncertainty of MDPs. However, batch-based DRL algorithms cannot guarantee the non-decreasing property of learned quantile curves especially at the early training stage, leading to abnormal distribution estimates and reduced model interpretability. To address these issues, we introduce a general DRL framework by using non-crossing quantile regression to ensure the monotonicity constraint within each sampled batch, which can be incorporated with any well-known DRL algorithm. We demonstrate the validity of our method from both the theory and model implementation perspectives. Experiments on Atari 2600 Games show that some state-of-art DRL algorithms with the non-crossing modification can significantly outperform their baselines in terms of faster convergence speeds and better testing performance. In particular, our method can effectively recover the distribution information and thus dramatically increase the exploration efficiency when the reward space is extremely sparse.

With the rapid advances in programmable materials, reconfigurable intelligent surfaces (RIS) have become a pivotal technology for future wireless communications. The simultaneous transmitting and reflecting reconfigurable intelligent surfaces (STAR-RIS) can both transmit and reflect signals, enabling comprehensive signal control and expanding application scenarios. This paper introduces an unmanned aerial vehicle (UAV) to further enhance system flexibility and proposes an optimization design for the spectrum efficiency of the STAR-RIS-UAV-assisted wireless communication system. We present a deep reinforcement learning (DRL) algorithm capable of iteratively optimizing beamforming, phase shifts, and UAV positioning to maximize the system's sum rate through continuous interactions with the environment. To improve exploration in deterministic policies, we introduce a stochastic perturbation factor, which enhances exploration capabilities. As exploration is strengthened, the algorithm's ability to accurately evaluate the state-action value function becomes critical. Thus, based on the deep deterministic policy gradient (DDPG) algorithm, we propose a convolution-augmented deep deterministic policy gradient (CA-DDPG) algorithm that balances exploration and evaluation to improve the system's sum rate. The simulation results demonstrate that the CA-DDPG algorithm effectively interacts with the environment, optimizing the beamforming matrix, phase shift matrix, and UAV location, thereby improving system capacity and achieving better performance than other algorithms.

Ridge leverage scores provide a balance between low-rank approximation and regularization, and are ubiquitous in randomized linear algebra and machine learning. Deterministic algorithms are also of interest in the moderately big data regime, because deterministic algorithms provide interpretability to the practitioner by having no failure probability and always returning the same results.

DDPG (TD3) [7], have demonstrated their great potential. Contributions . 1) We introduce a new, simple yet effective surrogate reward They usually proceed as follows.