We study policy gradient for mean-field control in continuous time in a reinforcement learning setting. By considering randomised policies with entropy regularisation, we derive a gradient expectation representation of the value function, which is amenable to actor-critic type algorithms, where the value functions and the policies are learnt alternately based on observation samples of the state and model-free estimation of the population state distribution, either by offline or online learning. In the linear-quadratic mean-field framework, we obtain an exact parametrisation of the actor and critic functions defined on the Wasserstein space. Finally, we illustrate the results of our algorithms with some numerical experiments on concrete examples.
Actor-critic deep reinforcement learning (DRL) algorithms have recently achieved prominent success in tackling various challenging reinforcement learning (RL) problems, particularly complex control tasks with high-dimensional continuous state and action spaces. Nevertheless, existing research showed that actor-critic DRL algorithms often failed to explore their learning environments effectively, resulting in limited learning stability and performance. To address this limitation, several ensemble DRL algorithms have been proposed lately to boost exploration and stabilize the learning process. However, most of existing ensemble algorithms do not explicitly train all base learners towards jointly optimizing the performance of the ensemble. In this paper, we propose a new technique to train an ensemble of base learners based on an innovative multi-step integration method. This training technique enables us to develop a new hierarchical learning algorithm for ensemble DRL that effectively promotes inter-learner collaboration through stable inter-learner parameter sharing. The design of our new algorithm is verified theoretically. The algorithm is also shown empirically to outperform several state-of-the-art DRL algorithms on multiple benchmark RL problems.
Inferring unknown constraints is a challenging and crucial problem in many robotics applications. When only expert demonstrations are available, it becomes essential to infer the unknown domain constraints to deploy additional agents effectively. In this work, we propose an approach to infer affine constraints in control tasks after observing expert demonstrations. We formulate the constraint inference problem as an inverse optimization problem, and we propose an alternating optimization scheme that infers the unknown constraints by minimizing a KKT residual objective. We demonstrate the effectiveness of our method in a number of simulations, and show that our method can infer less conservative constraints than a recent baseline method while maintaining comparable safety guarantees.
Many reinforcement learning (RL) applications have combinatorial action spaces, where each action is a composition of sub-actions. A standard RL approach ignores this inherent factorization structure, resulting in a potential failure to make meaningful inferences about rarely observed sub-action combinations; this is particularly problematic for offline settings, where data may be limited. In this work, we propose a form of linear Q-function decomposition induced by factored action spaces. We study the theoretical properties of our approach, identifying scenarios where it is guaranteed to lead to zero bias when used to approximate the Q-function. Outside the regimes with theoretical guarantees, we show that our approach can still be useful because it leads to better sample efficiency without necessarily sacrificing policy optimality, allowing us to achieve a better bias-variance trade-off. Across several offline RL problems using simulators and real-world datasets motivated by healthcare, we demonstrate that incorporating factored action spaces into value-based RL can result in better-performing policies. Our approach can help an agent make more accurate inferences within underexplored regions of the state-action space when applying RL to observational datasets.
The maximization of submodular functions have found widespread application in areas such as machine learning, combinatorial optimization, and economics, where practitioners often wish to enforce various constraints; the matroid constraint has been investigated extensively due to its algorithmic properties and expressive power. Recent progress has focused on fast algorithms for important classes of matroids given in explicit form. Currently, nearly-linear time algorithms only exist for graphic and partition matroids [ICALP '19]. In this work, we develop algorithms for monotone submodular maximization constrained by graphic, transversal matroids, or laminar matroids in time near-linear in the size of their representation. Our algorithms achieve an optimal approximation of $1-1/e-\epsilon$ and both generalize and accelerate the results of Ene and Nguyen [ICALP '19]. In fact, the running time of our algorithm cannot be improved within the fast continuous greedy framework of Badanidiyuru and Vondr\'ak [SODA '14]. To achieve near-linear running time, we make use of dynamic data structures that maintain bases with approximate maximum cardinality and weight under certain element updates. These data structures need to support a weight decrease operation and a novel FREEZE operation that allows the algorithm to freeze elements (i.e. force to be contained) in its basis regardless of future data structure operations. For the laminar matroid, we present a new dynamic data structure using the top tree interface of Alstrup, Holm, de Lichtenberg, and Thorup [TALG '05] that maintains the maximum weight basis under insertions and deletions of elements in $O(\log n)$ time. For the transversal matroid the FREEZE operation corresponds to requiring the data structure to keep a certain set $S$ of vertices matched, a property that we call $S$-stability.
We consider sequential state and parameter learning in state-space models with intractable state transition and observation processes. By exploiting low-rank tensor-train (TT) decompositions, we propose new sequential learning methods for joint parameter and state estimation under the Bayesian framework. Our key innovation is the introduction of scalable function approximation tools such as TT for recursively learning the sequentially updated posterior distributions. The function approximation perspective of our methods offers tractable error analysis and potentially alleviates the particle degeneracy faced by many particle-based methods. In addition to the new insights into algorithmic design, our methods complement conventional particle-based methods. Our TT-based approximations naturally define conditional Knothe--Rosenblatt (KR) rearrangements that lead to filtering, smoothing and path estimation accompanying our sequential learning algorithms, which open the door to removing potential approximation bias. We also explore several preconditioning techniques based on either linear or nonlinear KR rearrangements to enhance the approximation power of TT for practical problems. We demonstrate the efficacy and efficiency of our proposed methods on several state-space models, in which our methods achieve state-of-the-art estimation accuracy and computational performance.
The policy represented by the deep neural network can overfit the spurious features in observations, which hamper a reinforcement learning agent from learning effective policy. This issue becomes severe in high-dimensional state, where the agent struggles to learn a useful policy. Data augmentation can provide a performance boost to RL agents by mitigating the effect of overfitting. However, such data augmentation is a form of prior knowledge, and naively applying them in environments might worsen an agent's performance. In this paper, we propose a novel RL algorithm to mitigate the above issue and improve the efficiency of the learned policy. Our approach consists of a max-min game theoretic objective where a perturber network modifies the state to maximize the agent's probability of taking a different action while minimizing the distortion in the state. In contrast, the policy network updates its parameters to minimize the effect of perturbation while maximizing the expected future reward. Based on this objective, we propose a practical deep reinforcement learning algorithm, Adversarial Policy Optimization (APO). Our method is agnostic to the type of policy optimization, and thus data augmentation can be incorporated to harness the benefit. We evaluated our approaches on several DeepMind Control robotic environments with high-dimensional and noisy state settings. Empirical results demonstrate that our method APO consistently outperforms the state-of-the-art on-policy PPO agent. We further compare our method with state-of-the-art data augmentation, RAD, and regularization-based approach DRAC. Our agent APO shows better performance compared to these baselines.
The rapid changes in the finance industry due to the increasing amount of data have revolutionized the techniques on data processing and data analysis and brought new theoretical and computational challenges. In contrast to classical stochastic control theory and other analytical approaches for solving financial decision-making problems that heavily reply on model assumptions, new developments from reinforcement learning (RL) are able to make full use of the large amount of financial data with fewer model assumptions and to improve decisions in complex financial environments. This survey paper aims to review the recent developments and use of RL approaches in finance. We give an introduction to Markov decision processes, which is the setting for many of the commonly used RL approaches. Various algorithms are then introduced with a focus on value and policy based methods that do not require any model assumptions. Connections are made with neural networks to extend the framework to encompass deep RL algorithms. Our survey concludes by discussing the application of these RL algorithms in a variety of decision-making problems in finance, including optimal execution, portfolio optimization, option pricing and hedging, market making, smart order routing, and robo-advising.
The Q-learning algorithm is known to be affected by the maximization bias, i.e. the systematic overestimation of action values, an important issue that has recently received renewed attention. Double Q-learning has been proposed as an efficient algorithm to mitigate this bias. However, this comes at the price of an underestimation of action values, in addition to increased memory requirements and a slower convergence. In this paper, we introduce a new way to address the maximization bias in the form of a "self-correcting algorithm" for approximating the maximum of an expected value. Our method balances the overestimation of the single estimator used in conventional Q-learning and the underestimation of the double estimator used in Double Q-learning. Applying this strategy to Q-learning results in Self-correcting Q-learning. We show theoretically that this new algorithm enjoys the same convergence guarantees as Q-learning while being more accurate. Empirically, it performs better than Double Q-learning in domains with rewards of high variance, and it even attains faster convergence than Q-learning in domains with rewards of zero or low variance. These advantages transfer to a Deep Q Network implementation that we call Self-correcting DQN and which outperforms regular DQN and Double DQN on several tasks in the Atari 2600 domain.
Recommender systems play a crucial role in mitigating the problem of information overload by suggesting users' personalized items or services. The vast majority of traditional recommender systems consider the recommendation procedure as a static process and make recommendations following a fixed strategy. In this paper, we propose a novel recommender system with the capability of continuously improving its strategies during the interactions with users. We model the sequential interactions between users and a recommender system as a Markov Decision Process (MDP) and leverage Reinforcement Learning (RL) to automatically learn the optimal strategies via recommending trial-and-error items and receiving reinforcements of these items from users' feedbacks. In particular, we introduce an online user-agent interacting environment simulator, which can pre-train and evaluate model parameters offline before applying the model online. Moreover, we validate the importance of list-wise recommendations during the interactions between users and agent, and develop a novel approach to incorporate them into the proposed framework LIRD for list-wide recommendations. The experimental results based on a real-world e-commerce dataset demonstrate the effectiveness of the proposed framework.
Image segmentation is considered to be one of the critical tasks in hyperspectral remote sensing image processing. Recently, convolutional neural network (CNN) has established itself as a powerful model in segmentation and classification by demonstrating excellent performances. The use of a graphical model such as a conditional random field (CRF) contributes further in capturing contextual information and thus improving the segmentation performance. In this paper, we propose a method to segment hyperspectral images by considering both spectral and spatial information via a combined framework consisting of CNN and CRF. We use multiple spectral cubes to learn deep features using CNN, and then formulate deep CRF with CNN-based unary and pairwise potential functions to effectively extract the semantic correlations between patches consisting of three-dimensional data cubes. Effective piecewise training is applied in order to avoid the computationally expensive iterative CRF inference. Furthermore, we introduce a deep deconvolution network that improves the segmentation masks. We also introduce a new dataset and experimented our proposed method on it along with several widely adopted benchmark datasets to evaluate the effectiveness of our method. By comparing our results with those from several state-of-the-art models, we show the promising potential of our method.