We consider the combinatorial multi-armed bandit (CMAB) problem, where the reward function is nonlinear. In this setting, the agent chooses a batch of arms on each round and receives feedback from each arm of the batch. The reward that the agent aims to maximize is a function of the selected arms and their expectations. In many applications, the reward function is highly nonlinear, and the performance of existing algorithms relies on a global Lipschitz constant to encapsulate the function's nonlinearity. This may lead to loose regret bounds, since by itself, a large gradient does not necessarily cause a large regret, but only in regions where the uncertainty in the reward's parameters is high. To overcome this problem, we introduce a new smoothness criterion, which we term \emph{Gini-weighted smoothness}, that takes into account both the nonlinearity of the reward and concentration properties of the arms. We show that a linear dependence of the regret in the batch size in existing algorithms can be replaced by this smoothness parameter. This, in turn, leads to much tighter regret bounds when the smoothness parameter is batch-size independent. For example, in the probabilistic maximum coverage (PMC) problem, that has many applications, including influence maximization, diverse recommendations and more, we achieve dramatic improvements in the upper bounds. We also prove matching lower bounds for the PMC problem and show that our algorithm is tight, up to a logarithmic factor in the problem's parameters.
We consider the Inverse Reinforcement Learning (IRL) problem in Contextual Markov Decision Processes (CMDPs). Here, the reward of the environment, which is not available to the agent, depends on a static parameter referred to as the context. Each context defines an MDP (with a different reward signal), and the agent is provided demonstrations by an expert, for different contexts. The goal is to learn a mapping from contexts to rewards, such that planning with respect to the induced reward will perform similarly to the expert, even for unseen contexts. We suggest two learning algorithms for this scenario. (1) For rewards that are a linear function of the context, we provide a method that is guaranteed to return an $\epsilon$-optimal solution after a polynomial number of demonstrations. (2) For general reward functions, we propose black-box descent methods based on evolutionary strategies capable of working with nonlinear estimators (e.g., neural networks). We evaluate our algorithms in autonomous driving and medical treatment simulations and demonstrate their ability to learn and generalize to unseen contexts.
State-of-the-art efficient model-based Reinforcement Learning (RL) algorithms typically act by iteratively solving empirical models, i.e., by performing \emph{full-planning} on Markov Decision Processes (MDPs) built by the gathered experience. In this paper, we focus on model-based RL in the finite-state finite-horizon MDP setting and establish that exploring with \emph{greedy policies} -- act by \emph{1-step planning} -- can achieve tight minimax performance in terms of regret, $\tilde{\mathcal{O}}(\sqrt{HSAT})$. Thus, full-planning in model-based RL can be avoided altogether without any performance degradation, and, by doing so, the computational complexity decreases by a factor of $S$. The results are based on a novel analysis of real-time dynamic programming, then extended to model-based RL. Specifically, we generalize existing algorithms that perform full-planning to such that act by 1-step planning. For these generalizations, we prove regret bounds with the same rate as their full-planning counterparts.
We identify a fundamental problem in policy gradient-based methods in continuous control. As policy gradient methods require the agent's underlying probability distribution, they limit policy representation to parametric distribution classes. We show that optimizing over such sets results in local movement in the action space and thus convergence to sub-optimal solutions. We suggest a novel distributional framework, able to represent arbitrary distribution functions over the continuous action space. Using this framework, we construct a generative scheme, trained using an off-policy actor-critic paradigm, which we call the Generative Actor Critic (GAC). Compared to policy gradient methods, GAC does not require knowledge of the underlying probability distribution, thereby overcoming these limitations. Empirical evaluation shows that our approach is comparable and often surpasses current state-of-the-art baselines in continuous domains.
We propose a computationally efficient algorithm that combines compressed sensing with imitation learning to solve sequential decision making text-based games with combinatorial action spaces. We propose a variation of the compressed sensing algorithm Orthogonal Matching Pursuit (OMP), that we call IK-OMP, and show that it can recover a bag-of-words from a sum of the individual word embeddings, even in the presence of noise. We incorporate IK-OMP into a supervised imitation learning setting and show that this algorithm, called Sparse Imitation Learning (Sparse-IL), solves the entire text-based game of Zork1 with an action space of approximately 10 million actions using imperfect, noisy demonstrations.
Robust Markov Decision Processes (RMDPs) intend to ensure robustness with respect to changing or adversarial system behavior. In this framework, transitions are modeled as arbitrary elements of a known and properly structured uncertainty set and a robust optimal policy can be derived under the worst-case scenario. In this study, we address the issue of learning in RMDPs using a Bayesian approach. We introduce the Uncertainty Robust Bellman Equation (URBE) which encourages safe exploration for adapting the uncertainty set to new observations while preserving robustness. We propose a URBE-based algorithm, DQN-URBE, that scales this method to higher dimensional domains. Our experiments show that the derived URBE-based strategy leads to a better trade-off between less conservative solutions and robustness in the presence of model misspecification. In addition, we show that the DQN-URBE algorithm can adapt significantly faster to changing dynamics online compared to existing robust techniques with fixed uncertainty sets.
In e-commerce, product content, especially product images have a significant influence on a customer's journey from product discovery to evaluation and finally, purchase decision. Since many e-commerce retailers sell items from other third-party marketplace sellers besides their own, the content published by both internal and external content creators needs to be monitored and enriched, wherever possible. Despite guidelines and warnings, product listings that contain offensive and non-compliant images continue to enter catalogs. Offensive and non-compliant content can include a wide range of objects, logos, and banners conveying violent, sexually explicit, racist, or promotional messages. Such images can severely damage the customer experience, lead to legal issues, and erode the company brand. In this paper, we present a machine learning driven offensive and non-compliant image detection system for extremely large e-commerce catalogs. This system proactively detects and removes such content before they are published to the customer-facing website. This paper delves into the unique challenges of applying machine learning to real-world data from retail domain with hundreds of millions of product images. We demonstrate how we resolve the issue of non-compliant content that appears across tens of thousands of product categories. We also describe how we deal with the sheer variety in which each single non-compliant scenario appears. This paper showcases a number of practical yet unique approaches such as representative training data creation that are critical to solve an extremely rarely occurring problem. In summary, our system combines state-of-the-art image classification and object detection techniques, and fine tunes them with internal data to develop a solution customized for a massive, diverse, and constantly evolving product catalog.
We consider a sequential stochastic resource allocation problem under the gradient feedback, where the reward of each resource is concave. We construct a generic algorithm that is adaptive to the complexity of the problem, which is measured using the exponent in {\L}ojasiewicz inequality. Our algorithm interpolates between the non-strongly concave and the strongly-concave rates without depending on the strong-concavity parameter and recover the fast rate of classical multi-armed bandit (corresponding roughly to linear reward functions).