Tight Lower Bounds for Combinatorial Multi-Armed Bandits

The Combinatorial Multi-Armed Bandit problem is a sequential decision-making problem in which an agent selects a set of arms on each round, observes feedback for each of these arms and aims to maximize a known reward function of the arms it chose. While previous work proved regret upper bounds in this setting for general reward functions, only a few works provided matching lower bounds, all for specific reward functions. In this work, we prove regret lower bounds for combinatorial bandits that hold under mild assumptions for all smooth reward functions. We derive both problem-dependent and problem-independent bounds and show that the recently proposed Gini-weighted smoothness parameter \citep{merlisM19} also determines the lower bounds for monotone reward functions. Notably, this implies that our lower bounds are tight up to log-factors.

Patternless Adversarial Attacks on Video Recognition Networks

Deep neural networks for classification of videos, just like image classification networks, may be subjected to adversarial manipulation. The main difference between image classifiers and video classifiers is that the latter usually use temporal information contained within the video in the form of optical flow or implicitly by various differences between adjacent frames. In this work we present a manipulation scheme for fooling video classifiers by introducing a spatial patternless temporal perturbation that is practically unnoticed by human observers and undetectable by leading image adversarial pattern detection algorithms. After demonstrating the manipulation of action classification of single videos, we generalize the procedure to make adversarial patterns with temporal invariance that generalizes across different classes for both targeted and untargeted attacks.

Maximizing the Total Reward via Reward Tweaking

In reinforcement learning, the discount factor $\gamma$ controls the agent's effective planning horizon. Traditionally, this parameter was considered part of the MDP; however, as deep reinforcement learning algorithms tend to become unstable when the effective planning horizon is long, recent works refer to $\gamma$ as a hyper-parameter. In this work, we focus on the finite-horizon setting and introduce \emph{reward tweaking}. Reward tweaking learns a surrogate reward function $\tilde r$ for the discounted setting, which induces an optimal (undiscounted) return in the original finite-horizon task. Theoretically, we show that there exists a surrogate reward which leads to optimality in the original task and discuss the robustness of our approach. Additionally, we perform experiments in a high-dimensional continuous control task and show that reward tweaking guides the agent towards better long-horizon returns when it plans for short horizons using the tweaked reward.

Stabilizing Off-Policy Reinforcement Learning with Conservative Policy Gradients

In recent years, advances in deep learning have enabled the application of reinforcement learning algorithms in complex domains. However, they lack the theoretical guarantees which are present in the tabular setting and suffer from many stability and reproducibility problems \citep{henderson2018deep}. In this work, we suggest a simple approach for improving stability and providing probabilistic performance guarantees in off-policy actor-critic deep reinforcement learning regimes. Experiments on continuous action spaces, in the MuJoCo control suite, show that our proposed method reduces the variance of the process and improves the overall performance.

Natural Language State Representation for Reinforcement Learning

Recent advances in Reinforcement Learning have highlighted the difficulties in learning within complex high dimensional domains. We argue that one of the main reasons that current approaches do not perform well, is that the information is represented sub-optimally. A natural way to describe what we observe, is through natural language. In this paper, we implement a natural language state representation to learn and complete tasks. Our experiments suggest that natural language based agents are more robust, converge faster and perform better than vision based agents, showing the benefit of using natural language representations for Reinforcement Learning.

Multi-Step Greedy and Approximate Real Time Dynamic Programming

Real Time Dynamic Programming (RTDP) is a well-known Dynamic Programming (DP) based algorithm that combines planning and learning to find an optimal policy for an MDP. It is a planning algorithm because it uses the MDP's model (reward and transition functions) to calculate a 1-step greedy policy w.r.t.~an optimistic value function, by which it acts. It is a learning algorithm because it updates its value function only at the states it visits while interacting with the environment. As a result, unlike DP, RTDP does not require uniform access to the state space in each iteration, which makes it particularly appealing when the state space is large and simultaneously updating all the states is not computationally feasible. In this paper, we study a generalized multi-step greedy version of RTDP, which we call $h$-RTDP, in its exact form, as well as in three approximate settings: approximate model, approximate value updates, and approximate state abstraction. We analyze the sample, computation, and space complexities of $h$-RTDP and establish that increasing $h$ improves sample and space complexity, with the cost of additional offline computational operations. For the approximate cases, we prove that the asymptotic performance of $h$-RTDP is the same as that of a corresponding approximate DP -- the best one can hope for without further assumptions on the approximation errors. $h$-RTDP is the first algorithm with a provably improved sample complexity when increasing the lookahead horizon.

Off-Policy Evaluation in Partially Observable Environments

This work studies the problem of batch off-policy evaluation for Reinforcement Learning in partially observable environments. Off-policy evaluation under partial observability is inherently prone to bias, with risk of arbitrarily large errors. We define the problem of off-policy evaluation for Partially Observable Markov Decision Processes (POMDPs) and establish what we believe is the first off-policy evaluation result for POMDPs. In addition, we formulate a model in which observed and unobserved variables are decoupled into two dynamic processes, called a Decoupled POMDP. We show how off-policy evaluation can be performed under this new model, mitigating estimation errors inherent to the procedure we provided for general POMDPs. We demonstrate the pitfalls of off-policy evaluation in POMDPs using a well-known off-policy method, importance sampling, and compare with our result on synthetic medical data.

Adaptive Trust Region Policy Optimization: Global Convergence and Faster Rates for Regularized MDPs

Trust region policy optimization (TRPO) is a popular and empirically successful policy search algorithm in Reinforcement Learning (RL) in which a surrogate problem, that restricts consecutive policies to be `close' to one another, is iteratively solved. Nevertheless, TRPO has been considered a heuristic algorithm inspired by Conservative Policy Iteration (CPI). We show that the adaptive scaling mechanism used in TRPO is in fact the natural "RL version" of traditional trust-region methods from convex analysis. We first analyze TRPO in the planning setting, in which we have access to the model and the entire state space. Then, we consider sample-based TRPO and establish $\tilde O(1/\sqrt{N})$ convergence rate to the global optimum. Importantly, the adaptive scaling mechanism allows us to analyze TRPO in {\em regularized MDPs} for which we prove fast rates of $\tilde O(1/N)$, much like results in convex optimization. This is the first result in RL of better rates when regularizing the instantaneous cost or reward.

Practical Risk Measures in Reinforcement Learning

Practical application of Reinforcement Learning (RL) often involves risk considerations. We study a generalized approximation scheme for risk measures, based on Monte-Carlo simulations, where the risk measures need not necessarily be \emph{coherent}. We demonstrate that, even in simple problems, measures such as the variance of the reward-to-go do not capture the risk in a satisfactory manner. In addition, we show how a risk measure can be derived from model's realizations. We propose a neural architecture for estimating the risk and suggest the risk critic architecture that can be use to optimize a policy under general risk measures. We conclude our work with experiments that demonstrate the efficacy of our approach.

Topic Modeling via Full Dependence Mixtures

We consider the topic modeling problem for large datasets. For this problem, Latent Dirichlet Allocation (LDA) with a collapsed Gibbs sampler optimization is the state-of-the-art approach in terms of topic quality. However, LDA is a slow approach, and running it on large datasets is impractical even with modern hardware. In this paper we propose to fit topics directly to the co-occurances data of the corpus. In particular, we introduce an extension of a mixture model, the Full Dependence Mixture (FDM), which arises naturally as a model of a second moment under general generative assumptions on the data. While there is some previous work on topic modeling using second moments, we develop a direct stochastic optimization procedure for fitting an FDM with a single Kullback Leibler objective. While moment methods in general have the benefit that an iteration no longer needs to scale with the size of the corpus, our approach also allows us to leverage standard optimizers and GPUs for the problem of topic modeling. We evaluate the approach on synthetic and semi-synthetic data, as well as on the SOTU and Neurips Papers corpora, and show that the approach outperforms LDA, where LDA is run on both full and sub-sampled data.