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We study zero-shot generalization in reinforcement learning - optimizing a policy on a set of training tasks such that it will perform well on a similar but unseen test task. To mitigate overfitting, previous work explored different notions of invariance to the task. However, on problems such as the ProcGen Maze, an adequate solution that is invariant to the task visualization does not exist, and therefore invariance-based approaches fail. Our insight is that learning a policy that $\textit{explores}$ the domain effectively is harder to memorize than a policy that maximizes reward for a specific task, and therefore we expect such learned behavior to generalize well; we indeed demonstrate this empirically on several domains that are difficult for invariance-based approaches. Our $\textit{Explore to Generalize}$ algorithm (ExpGen) builds on this insight: We train an additional ensemble of agents that optimize reward. At test time, either the ensemble agrees on an action, and we generalize well, or we take exploratory actions, which are guaranteed to generalize and drive us to a novel part of the state space, where the ensemble may potentially agree again. We show that our approach is the state-of-the-art on several tasks in the ProcGen challenge that have so far eluded effective generalization. For example, we demonstrate a success rate of $82\%$ on the Maze task and $74\%$ on Heist with $200$ training levels.

We propose a novel alternative approach to our previous work (Ben Hammouda et al., 2023) to improve the efficiency of Monte Carlo (MC) estimators for rare event probabilities for stochastic reaction networks (SRNs). In the same spirit of (Ben Hammouda et al., 2023), an efficient path-dependent measure change is derived based on a connection between determining optimal importance sampling (IS) parameters within a class of probability measures and a stochastic optimal control formulation, corresponding to solving a variance minimization problem. In this work, we propose a novel approach to address the encountered curse of dimensionality by mapping the problem to a significantly lower-dimensional space via a Markovian projection (MP) idea. The output of this model reduction technique is a low-dimensional SRN (potentially even one dimensional) that preserves the marginal distribution of the original high-dimensional SRN system. The dynamics of the projected process are obtained by solving a related optimization problem via a discrete $L^2$ regression. By solving the resulting projected Hamilton-Jacobi-Bellman (HJB) equations for the reduced-dimensional SRN, we obtain projected IS parameters, which are then mapped back to the original full-dimensional SRN system, resulting in an efficient IS-MC estimator for rare events probabilities of the full-dimensional SRN. Our analysis and numerical experiments reveal that the proposed MP-HJB-IS approach substantially reduces the MC estimator variance, resulting in a lower computational complexity in the rare event regime than standard MC estimators.

We study reinforcement learning (RL) in the setting of continuous time and space, for an infinite horizon with a discounted objective and the underlying dynamics driven by a stochastic differential equation. Built upon recent advances in the continuous approach to RL, we develop a notion of occupation time (specifically for a discounted objective), and show how it can be effectively used to derive performance-difference and local-approximation formulas. We further extend these results to illustrate their applications in the PG (policy gradient) and TRPO/PPO (trust region policy optimization/ proximal policy optimization) methods, which have been familiar and powerful tools in the discrete RL setting but under-developed in continuous RL. Through numerical experiments, we demonstrate the effectiveness and advantages of our approach.

We study single-machine scheduling of jobs, each belonging to a job type that determines its duration distribution. We start by analyzing the scenario where the type characteristics are known and then move to two learning scenarios where the types are unknown: non-preemptive problems, where each started job must be completed before moving to another job; and preemptive problems, where job execution can be paused in the favor of moving to a different job. In both cases, we design algorithms that achieve sublinear excess cost, compared to the performance with known types, and prove lower bounds for the non-preemptive case. Notably, we demonstrate, both theoretically and through simulations, how preemptive algorithms can greatly outperform non-preemptive ones when the durations of different job types are far from one another, a phenomenon that does not occur when the type durations are known.

Recent advances in visual reinforcement learning (RL) have led to impressive success in handling complex tasks. However, these methods have demonstrated limited generalization capability to visual disturbances, which poses a significant challenge for their real-world application and adaptability. Though normalization techniques have demonstrated huge success in supervised and unsupervised learning, their applications in visual RL are still scarce. In this paper, we explore the potential benefits of integrating normalization into visual RL methods with respect to generalization performance. We find that, perhaps surprisingly, incorporating suitable normalization techniques is sufficient to enhance the generalization capabilities, without any additional special design. We utilize the combination of two normalization techniques, CrossNorm and SelfNorm, for generalizable visual RL. Extensive experiments are conducted on DMControl Generalization Benchmark and CARLA to validate the effectiveness of our method. We show that our method significantly improves generalization capability while only marginally affecting sample efficiency. In particular, when integrated with DrQ-v2, our method enhances the test performance of DrQ-v2 on CARLA across various scenarios, from 14% of the training performance to 97%.

Graph mining tasks arise from many different application domains, ranging from social networks, transportation, E-commerce, etc., which have been receiving great attention from the theoretical and algorithm design communities in recent years, and there has been some pioneering work using the hotly researched reinforcement learning (RL) techniques to address graph data mining tasks. However, these graph mining algorithms and RL models are dispersed in different research areas, which makes it hard to compare different algorithms with each other. In this survey, we provide a comprehensive overview of RL models and graph mining and generalize these algorithms to Graph Reinforcement Learning (GRL) as a unified formulation. We further discuss the applications of GRL methods across various domains and summarize the method description, open-source codes, and benchmark datasets of GRL methods. Finally, we propose possible important directions and challenges to be solved in the future. This is the latest work on a comprehensive survey of GRL literature, and this work provides a global view for researchers as well as a learning resource for researchers outside the domain. In addition, we create an online open-source for both interested researchers who want to enter this rapidly developing domain and experts who would like to compare GRL methods.

In this monograph, I introduce the basic concepts of Online Learning through a modern view of Online Convex Optimization. Here, online learning refers to the framework of regret minimization under worst-case assumptions. I present first-order and second-order algorithms for online learning with convex losses, in Euclidean and non-Euclidean settings. All the algorithms are clearly presented as instantiation of Online Mirror Descent or Follow-The-Regularized-Leader and their variants. Particular attention is given to the issue of tuning the parameters of the algorithms and learning in unbounded domains, through adaptive and parameter-free online learning algorithms. Non-convex losses are dealt through convex surrogate losses and through randomization. The bandit setting is also briefly discussed, touching on the problem of adversarial and stochastic multi-armed bandits. These notes do not require prior knowledge of convex analysis and all the required mathematical tools are rigorously explained. Moreover, all the proofs have been carefully chosen to be as simple and as short as possible.

Clustering is one of the most fundamental and wide-spread techniques in exploratory data analysis. Yet, the basic approach to clustering has not really changed: a practitioner hand-picks a task-specific clustering loss to optimize and fit the given data to reveal the underlying cluster structure. Some types of losses---such as k-means, or its non-linear version: kernelized k-means (centroid based), and DBSCAN (density based)---are popular choices due to their good empirical performance on a range of applications. Although every so often the clustering output using these standard losses fails to reveal the underlying structure, and the practitioner has to custom-design their own variation. In this work we take an intrinsically different approach to clustering: rather than fitting a dataset to a specific clustering loss, we train a recurrent model that learns how to cluster. The model uses as training pairs examples of datasets (as input) and its corresponding cluster identities (as output). By providing multiple types of training datasets as inputs, our model has the ability to generalize well on unseen datasets (new clustering tasks). Our experiments reveal that by training on simple synthetically generated datasets or on existing real datasets, we can achieve better clustering performance on unseen real-world datasets when compared with standard benchmark clustering techniques. Our meta clustering model works well even for small datasets where the usual deep learning models tend to perform worse.