Resolving the exploration-exploitation trade-off remains a fundamental problem in the design and implementation of reinforcement learning (RL) algorithms. In this paper, we focus on model-free RL using the epsilon-greedy exploration policy, which despite its simplicity, remains one of the most frequently used forms of exploration. However, a key limitation of this policy is the specification of $\varepsilon$. In this paper, we provide a novel Bayesian perspective of $\varepsilon$ as a measure of the uniformity of the Q-value function. We introduce a closed-form Bayesian model update based on Bayesian model combination (BMC), based on this new perspective, which allows us to adapt $\varepsilon$ using experiences from the environment in constant time with monotone convergence guarantees. We demonstrate that our proposed algorithm, $\varepsilon$-\texttt{BMC}, efficiently balances exploration and exploitation on different problems, performing comparably or outperforming the best tuned fixed annealing schedules and an alternative data-dependent $\varepsilon$ adaptation scheme proposed in the literature.
Multi-agent reinforcement learning (MARL) can model many real world applications. However, many MARL approaches rely on epsilon greedy for exploration, which may discourage visiting advantageous states in hard scenarios. In this paper, we propose a new approach QMIX(SEG) for tackling MARL. It makes use of the value function factorization method QMIX to train per-agent policies and a novel Semantic Epsilon Greedy (SEG) exploration strategy. SEG is a simple extension to the conventional epsilon greedy exploration strategy, yet it is experimentally shown to greatly improve the performance of MARL…
University of Maryland, College Park（马里兰大学帕克分校）；Department of Mathematics, University of Maryland, College Park（马里兰大学帕克分校数学系）
Policy learning is a quickly growing area. As robotics and computers control day-to-day life, their error rate needs to be minimized and controlled. There are many policy learning methods and bandit methods with provable error rates that accompany them. We show an error or regret bound and convergence of the Deep Epsilon Greedy method which chooses actions with a neural network's prediction. We also show that Epsilon Greedy method regret upper bound is minimized with cubic root exploration. In experiments with the real-world dataset MNIST, we construct a nonlinear reinforcement learning proble…
Google Research（谷歌研究院）；Tel Aviv University（特拉维夫大学）；Courant Institute of Mathematical Sciences（柯朗数学科学研究所）；Cornell University（康奈尔大学）
Myopic exploration policies such as epsilon-greedy, softmax, or Gaussian noise fail to explore efficiently in some reinforcement learning tasks and yet, they perform well in many others. In fact, in practice, they are often selected as the top choices, due to their simplicity. But, for what tasks do such policies succeed? Can we give theoretical guarantees for their favorable performance? These crucial questions have been scarcely investigated, despite the prominent practical importance of these policies. This paper presents a theoretical analysis of such policies and provides the first regret…
This paper explores multi-armed bandit (MAB) strategies in very short horizon scenarios, i.e., when the bandit strategy is only allowed very few interactions with the environment. This is an understudied setting in the MAB literature with many applications in the context of games, such as player modeling. Specifically, we pursue three different ideas. First, we explore the use of regression oracles, which replace the simple average used in strategies such as epsilon-greedy with linear regression models. Second, we examine different exploration patterns such as forced exploration phases. Finall…
Contextual multi-armed bandit problems arise frequently in important industrial applications. Existing solutions model the context either linearly, which enables uncertainty driven (principled) exploration, or non-linearly, by using epsilon-greedy exploration policies. Here we present a deep learning framework for contextual multi-armed bandits that is both non-linear and enables principled exploration at the same time. We tackle the exploration vs. exploitation trade-off through Thompson sampling by exploiting the connection between inference time dropout and sampling from the posterior over …
Bayesian strategies for contextual bandits have proved promising in single-state reinforcement learning tasks by modeling uncertainty using context information from the environment. In this paper, we propose Greedy Bandits with Sampled Context (GB-SC), a method for contextual multi-armed bandits to develop the prior from the context information using Thompson Sampling, and arm selection using an epsilon-greedy policy. The framework GB-SC allows for evaluation of context-reward dependency, as well as providing robustness for partially observable context vectors by leveraging the prior developed…
Princeton University（普林斯顿大学）；Samsung AI Center NYC（三星人工智能中心（纽约））；Stanford University（斯坦福大学）
A major challenge in reinforcement learning is exploration, when local dithering methods such as epsilon-greedy sampling are insufficient to solve a given task. Many recent methods have proposed to intrinsically motivate an agent to seek novel states, driving the agent to discover improved reward. However, while state-novelty exploration methods are suitable for tasks where novel observations correlate well with improved reward, they may not explore more efficiently than epsilon-greedy approaches in environments where the two are not well-correlated. In this paper, we distinguish between explo…
Missouri University of S&T（密苏里科技大学）；University of California, Riverside（加州大学河滨分校）
In this paper, a MIMO simulated annealing SA based Q learning method is proposed to control a line follower robot. The conventional controller for these types of robots is the proportional P controller. Considering the unknown mechanical characteristics of the robot and uncertainties such as friction and slippery surfaces, system modeling and controller designing can be extremely challenging. The mathematical modeling for the robot is presented in this paper, and a simulator is designed based on this model. The basic Q learning methods are based pure exploitation and the epsilon-greedy methods…
Exploration is a difficult challenge in reinforcement learning and even recent state-of-the art curiosity-based methods rely on the simple epsilon-greedy strategy to generate novelty. We argue that pure random walks do not succeed to properly expand the exploration area in most environments and propose to replace single random action choices by random goals selection followed by several steps in their direction. This approach is compatible with any curiosity-based exploration and off-policy reinforcement learning agents and generates longer and safer trajectories than individual random actions…
In the search and retrieval of multimedia objects, it is impractical to either manually or automatically extract the contents for indexing since most of the multimedia contents are not machine extractable, while manual extraction tends to be highly laborious and time-consuming. However, by systematically capturing and analyzing the feedback patterns of human users, vital information concerning the multimedia contents can be harvested for effective indexing and subsequent search. By learning from the human judgment and mental evaluation of users, effective search indices can be gradually develo…
Exploration is a difficult challenge in reinforcement learning and is of prime importance in sparse reward environments. However, many of the state of the art deep reinforcement learning algorithms, that rely on epsilon-greedy, fail on these environments. In such cases, empowerment can serve as an intrinsic reward signal to enable the agent to maximize the influence it has over the near future. We formulate empowerment as the channel capacity between states and actions and is calculated by estimating the mutual information between the actions and the following states. The mutual information is…
UC Berkeley, Department of Electrical Engineering and Computer Sciences（加州大学伯克利分校电气工程与计算机科学系）；Ghent University - imec, Department of Information Technology（根特大学-imec，信息技术系）；OpenAI
Scalable and effective exploration remains a key challenge in reinforcement learning (RL). While there are methods with optimality guarantees in the setting of discrete state and action spaces, these methods cannot be applied in high-dimensional deep RL scenarios. As such, most contemporary RL relies on simple heuristics such as epsilon-greedy exploration or adding Gaussian noise to the controls. This paper introduces Variational Information Maximizing Exploration (VIME), an exploration strategy based on maximization of information gain about the agent's belief of environment dynamics. We prop…
An automatic program that generates constant profit from the financial market is lucrative for every market practitioner. Recent advance in deep reinforcement learning provides a framework toward end-to-end training of such trading agent. In this paper, we propose an Markov Decision Process (MDP) model suitable for the financial trading task and solve it with the state-of-the-art deep recurrent Q-network (DRQN) algorithm. We propose several modifications to the existing learning algorithm to make it more suitable under the financial trading setting, namely 1. We employ a substantially small re…
The Multi-armed bandit offer the advantage to learn and exploit the already learnt knowledge at the same time. This capability allows this approach to be applied in different domains, going from clinical trials where the goal is investigating the effects of different experimental treatments while minimizing patient losses, to adaptive routing where the goal is to minimize the delays in a network. This article provides a review of the recent results on applying bandit to real-life scenario and summarize the state of the art for each of these fields. Different techniques has been proposed to sol…
Inria（法国国家信息与自动化研究所）；Ecole Polytechnique（巴黎综合理工学院）；CNRS（法国国家科学研究中心）；Université de Lille（里尔大学）；Google Research（谷歌研究院）
Incorporating prior knowledge in reinforcement learning algorithms is mainly an open question. Even when insights about the environment dynamics are available, reinforcement learning is traditionally used in a tabula rasa setting and must explore and learn everything from scratch. In this paper, we consider the problem of exploiting priors about action sequence equivalence: that is, when different sequences of actions produce the same effect. We propose a new local exploration strategy calibrated to minimize collisions and maximize new state visitations. We show that this strategy can be compu…
Volvo Car Corporation（沃尔沃汽车公司）；Chalmers University of Technology（查尔姆斯理工大学）
In this work, we address the problem of long-distance navigation for battery electric vehicles (BEVs), where one or more charging sessions are required to reach the intended destination. We consider the availability and performance of the charging stations to be unknown and stochastic, and develop a combinatorial semi-bandit framework for exploring the road network to learn the parameters of the queue time and charging power distributions. Within this framework, we first outline a pre-processing for the road network graph to handle the constrained combinatorial optimization problem in an effic…
In statistical dialogue management, the dialogue manager learns a policy that maps a belief state to an action for the system to perform. Efficient exploration is key to successful policy optimisation. Current deep reinforcement learning methods are very promising but rely on epsilon-greedy exploration, thus subjecting the user to a random choice of action during learning. Alternative approaches such as Gaussian Process SARSA (GPSARSA) estimate uncertainties and are sample efficient, leading to better user experience, but on the expense of a greater computational complexity. This paper examine…
Being able to reach any desired location in the environment can be a valuable asset for an agent. Learning a policy to navigate between all pairs of states individually is often not feasible. An all-goals updating algorithm uses each transition to learn Q-values towards all goals simultaneously and off-policy. However the expensive numerous updates in parallel limited the approach to small tabular cases so far. To tackle this problem we propose to use convolutional network architectures to generate Q-values and updates for a large number of goals at once. We demonstrate the accuracy and genera…
Indian Institute of Technology Kharagpur（印度理工学院卡哈拉格普尔分校）；Google Research（谷歌研究院）
In this work we present a novel approach for transfer-guided exploration in reinforcement learning that is inspired by the human tendency to leverage experiences from similar encounters in the past while navigating a new task. Given an optimal policy in a related task-environment, we show that its bisimulation distance from the current task-environment gives a lower bound on the optimal advantage of state-action pairs in the current task-environment. Transfer-guided Exploration (ExTra) samples actions from a Softmax distribution over these lower bounds. In this way, actions with potentially hi…
Achieving efficient and scalable exploration in complex domains poses a major challenge in reinforcement learning. While Bayesian and PAC-MDP approaches to the exploration problem offer strong formal guarantees, they are often impractical in higher dimensions due to their reliance on enumerating the state-action space. Hence, exploration in complex domains is often performed with simple epsilon-greedy methods. In this paper, we consider the challenging Atari games domain, which requires processing raw pixel inputs and delayed rewards. We evaluate several more sophisticated exploration strategi…
Edge Computing (EC) offers a superior user experience by positioning cloud resources in close proximity to end users. The challenge of allocating edge resources efficiently while maximizing profit for the EC platform remains a sophisticated problem, especially with the added complexity of the online arrival of resource requests. To address this challenge, we propose to cast the problem as a multi-armed bandit problem and develop two novel online pricing mechanisms, the Kullback-Leibler Upper Confidence Bound (KL-UCB) algorithm and the Min-Max Optimal algorithm, for heterogeneous edge resource …
ETH Zurich（苏黎世联邦理工学院）；Massachusetts Institute of Technology（麻省理工学院）；École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
We consider decentralized stochastic multi-armed bandit problem with multiple players in the case of different communication probabilities between players. Each player makes a decision of pulling an arm without cooperation while aiming to maximize his or her reward but informs his or her neighbors in the end of every turn about the arm he or she pulled and the reward he or she got. Neighbors of players are determined according to an Erdos-Renyi graph with which is reproduced in the beginning of every turn. We consider i.i.d. rewards generated by a Bernoulli distribution and assume that players…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
In this paper, we propose a novel neural exploration strategy in contextual bandits, EE-Net, distinct from the standard UCB-based and TS-based approaches. Contextual multi-armed bandits have been studied for decades with various applications. To solve the exploitation-exploration tradeoff in bandits, there are three main techniques: epsilon-greedy, Thompson Sampling (TS), and Upper Confidence Bound (UCB). In recent literature, linear contextual bandits have adopted ridge regression to estimate the reward function and combine it with TS or UCB strategies for exploration. However, this line of w…
We consider the problem of selecting a seed set to maximize the expected number of influenced nodes in the social network, referred to as the \textit{influence maximization} (IM) problem. We assume that the topology of the social network is prescribed while the influence probabilities among edges are unknown. In order to learn the influence probabilities and simultaneously maximize the influence spread, we consider the tradeoff between exploiting the current estimation of the influence probabilities to ensure certain influence spread and exploring more nodes to learn better about the influence…
Designing efficient exploration is central to Reinforcement Learning due to the fundamental problem posed by the exploration-exploitation dilemma. Bayesian exploration strategies like Thompson Sampling resolve this trade-off in a principled way by modeling and updating the distribution of the parameters of the action-value function, the outcome model of the environment. However, this technique becomes infeasible for complex environments due to the computational intractability of maintaining probability distributions over parameters of outcome models of corresponding complexity. Moreover, the a…
The exploration/exploitation (E/E) dilemma arises naturally in many subfields of Science. Multi-armed bandit problems formalize this dilemma in its canonical form. Most current research in this field focuses on generic solutions that can be applied to a wide range of problems. However, in practice, it is often the case that a form of prior information is available about the specific class of target problems. Prior knowledge is rarely used in current solutions due to the lack of a systematic approach to incorporate it into the E/E strategy. To address a specific class of E/E problems, we propos…
University of Tübingen（图宾根大学）；University of Twente（特文特大学）；University of Amsterdam（阿姆斯特丹大学）
In this work, we ask for and answer what makes classical temporal-difference reinforcement learning with epsilon-greedy strategies cooperative. Cooperating in social dilemma situations is vital for animals, humans, and machines. While evolutionary theory revealed a range of mechanisms promoting cooperation, the conditions under which agents learn to cooperate are contested. Here, we demonstrate which and how individual elements of the multi-agent learning setting lead to cooperation. We use the iterated Prisoner's dilemma with one-period memory as a testbed. Each of the two learning agents lea…
Although many algorithms for the multi-armed bandit problem are well-understood theoretically, empirical confirmation of their effectiveness is generally scarce. This paper presents a thorough empirical study of the most popular multi-armed bandit algorithms. Three important observations can be made from our results. Firstly, simple heuristics such as epsilon-greedy and Boltzmann exploration outperform theoretically sound algorithms on most settings by a significant margin. Secondly, the performance of most algorithms varies dramatically with the parameters of the bandit problem. Our study ide…
A Reinforcement Learning (RL) system depends on a set of initial conditions (hyperparameters) that affect the system's performance. However, defining a good choice of hyperparameters is a challenging problem. Hyperparameter tuning often requires manual or automated searches to find optimal values. Nonetheless, a noticeable limitation is the high cost of algorithm evaluation for complex models, making the tuning process computationally expensive and time-consuming. In this paper, we propose a framework based on integrating complex event processing and temporal models, to alleviate these trade-o…
Reinforcement Learning (RL) is a general framework concerned with an agent that seeks to maximize rewards in an environment. The learning typically happens through trial and error using explorative methods, such as epsilon-greedy. There are two approaches, model-based and model-free reinforcement learning, that show concrete results in several disciplines. Model-based RL learns a model of the environment for learning the policy while model-free approaches are fully explorative and exploitative without considering the underlying environment dynamics. Model-free RL works conceptually well in sim…
E-commerce sites strive to provide users the most timely relevant information in order to reduce shopping frictions and increase customer satisfaction. Multi armed bandit models (MAB) as a type of adaptive optimization algorithms provide possible approaches for such purposes. In this paper, we analyze using three classic MAB algorithms, epsilon-greedy, Thompson sampling (TS), and upper confidence bound 1 (UCB1) for dynamic content recommendations, and walk through the process of developing these algorithms internally to solve a real world e-commerce use case. First, we analyze the three MAB al…
University of Padova（帕多瓦大学）；Czech Technical University in Prague（布拉格捷克理工大学）
Optimization problems with set submodular objective functions have many real-world applications. In discrete scenarios, where the same item can be selected more than once, the domain is generalized from a 2-element set to a bounded integer lattice. In this work, we consider the problem of maximizing a monotone submodular function on the bounded integer lattice subject to a cardinality constraint. In particular, we focus on maximizing DR-submodular functions, i.e., functions defined on the integer lattice that exhibit the diminishing returns property. Given any epsilon > 0, we present a randomi…
Meta-learning empowers artificial intelligence to increase its efficiency by learning how to learn. Unlocking this potential involves overcoming a challenging meta-optimisation problem. We propose an algorithm that tackles this problem by letting the meta-learner teach itself. The algorithm first bootstraps a target from the meta-learner, then optimises the meta-learner by minimising the distance to that target under a chosen (pseudo-)metric. Focusing on meta-learning with gradients, we establish conditions that guarantee performance improvements and show that the metric can control meta-optim…
