For researchers and practitioners in finance, finding synergistic formulaic alphas is very important but challenging. In this paper, we reconsider the discovery of synergistic formulaic alphas from the viewpoint of sequential decision-making, and conceptualize the entire alpha discovery process as a non-stationary and reward-sparse Markov decision process. To overcome the challenges of non-stationarity and reward-sparsity, we propose the AlphaQCM method, a novel distributional reinforcement learning method designed to search for synergistic formulaic alphas efficiently. The AlphaQCM method first learns the Q function and quantiles via a Q network and a quantile network, respectively. Then, the AlphaQCM method applies the quantiled conditional moment method to learn unbiased variance from the potentially biased quantiles. Guided by the learned Q function and variance, the AlphaQCM method navigates the non-stationarity and reward-sparsity to explore the vast search space of formulaic alphas with high efficacy. Empirical applications to real-world datasets demonstrate that our AlphaQCM method significantly outperforms its competitors, particularly when dealing with large datasets comprising numerous stocks.

A key challenge in offline reinforcement learning (RL) is how to ensure the learned offline policy is safe, especially in safety-critical domains. In this article, we focus on learning a distributional value function in offline RL and optimizing a worst-case criterion of returns. However, optimizing a distributional value function in offline RL can be hard, since the crossing quantile issue is serious, and the distribution shift problem needs to be addressed. To this end, we propose monotonic quantile network (MQN) with conservative quantile regression (CQR) for risk-averse policy learning. First, we propose an MQN to learn the distribution over returns with non-crossing guarantees of the quantiles. Then, we perform CQR by penalizing the quantile estimation for out-of-distribution (OOD) actions to address the distribution shift in offline RL. Finally, we learn a worst-case policy by optimizing the conditional value-at-risk (CVaR) of the distributional value function. Furthermore, we provide theoretical analysis of the fixed-point convergence in our method. We conduct experiments in both risk-neutral and risk-sensitive offline settings, and the results show that our method obtains safe and conservative behaviors in robotic locomotion tasks.

Although distributional reinforcement learning (DRL) has been widely examined in the past few years, very few studies investigate the validity of the obtained Q-function estimator in the distributional setting. To fully understand how the approximation errors of the Q-function affect the whole training process, we do some error analysis and theoretically show how to reduce both the bias and the variance of the error terms. With this new understanding, we construct a new estimator Quantiled Expansion Mean (QEM) and introduce a new DRL algorithm (QEMRL) from the statistical perspective. We extensively evaluate our QEMRL algorithm on a variety of Atari and Mujoco benchmark tasks and demonstrate that QEMRL achieves significant improvement over baseline algorithms in terms of sample efficiency and convergence performance.

Although distributional reinforcement learning (DRL) has been widely examined in the past few years, there are two open questions people are still trying to address. One is how to ensure the validity of the learned quantile function, the other is how to efficiently utilize the distribution information. This paper attempts to provide some new perspectives to encourage the future in-depth studies in these two fields. We first propose a non-decreasing quantile function network (NDQFN) to guarantee the monotonicity of the obtained quantile estimates and then design a general exploration framework called distributional prediction error (DPE) for DRL which utilizes the entire distribution of the quantile function. In this paper, we not only discuss the theoretical necessity of our method but also show the performance gain it achieves in practice by comparing with some competitors on Atari 2600 Games especially in some hard-explored games.