arXiv subjects

Shie Mannor

Publications and source records attributed to Shie Mannor.

At least 181 records · Page 10Linked to original sources

arXiv2017

Situationally Aware Options

Hierarchical abstractions, also known as options -- a type of temporally extended action (Sutton et. al. 1999) that enables a reinforcement learning agent to plan at a higher level, abstracting away from the lower-level details. In this work, we learn reusable options whose parameters can vary, encouraging different behaviors, based on the current situation. In principle, these behaviors can include vigor, defence or even risk-averseness. These are some examples of what we refer to in the broader context as Situational Awareness (SA). We incorporate SA, in the form of vigor, into hierarchical RL by defining and learning situationally aware options in a Probabilistic Goal Semi-Markov Decision Process (PG-SMDP). This is achieved using our Situationally Aware oPtions (SAP) policy gradient algorithm which comes with a theoretical convergence guarantee. We learn reusable options in different scenarios in a RoboCup soccer domain (i.e., winning/losing). These options learn to execute with different levels of vigor resulting in human-like behaviours such as `time-wasting' in the winning scenario. We show the potential of the agent to exit bad local optima using reusable options in RoboCup. Finally, using SAP, the agent mitigates feature-based model misspecification in a Bottomless Pit of Death domain.

cs.AI↗

arXiv2017

Ensemble Robustness and Generalization of Stochastic Deep Learning Algorithms

The question why deep learning algorithms generalize so well has attracted increasing research interest. However, most of the well-established approaches, such as hypothesis capacity, stability or sparseness, have not provided complete explanations (Zhang et al., 2016; Kawaguchi et al., 2017). In this work, we focus on the robustness approach (Xu & Mannor, 2012), i.e., if the error of a hypothesis will not change much due to perturbations of its training examples, then it will also generalize well. As most deep learning algorithms are stochastic (e.g., Stochastic Gradient Descent, Dropout, and Bayes-by-backprop), we revisit the robustness arguments of Xu & Mannor, and introduce a new approach, ensemble robustness, that concerns the robustness of a population of hypotheses. Through the lens of ensemble robustness, we reveal that a stochastic learning algorithm can generalize well as long as its sensitiveness to adversarial perturbations is bounded in average over training examples. Moreover, an algorithm may be sensitive to some adversarial examples (Goodfellow et al., 2015) but still generalize well. To support our claims, we provide extensive simulations for different deep learning algorithms and different network architectures exhibiting a strong correlation between ensemble robustness and the ability to generalize.

cs.LG↗

arXiv2017

Rotting Bandits

The Multi-Armed Bandits (MAB) framework highlights the tension between acquiring new knowledge (Exploration) and leveraging available knowledge (Exploitation). In the classical MAB problem, a decision maker must choose an arm at each time step, upon which she receives a reward. The decision maker's objective is to maximize her cumulative expected reward over the time horizon. The MAB problem has been studied extensively, specifically under the assumption of the arms' rewards distributions being stationary, or quasi-stationary, over time. We consider a variant of the MAB framework, which we termed Rotting Bandits, where each arm's expected reward decays as a function of the number of times it has been pulled. We are motivated by many real-world scenarios such as online advertising, content recommendation, crowdsourcing, and more. We present algorithms, accompanied by simulations, and derive theoretical guarantees.

stat.ML↗

arXiv2017

Shallow Updates for Deep Reinforcement Learning

Deep reinforcement learning (DRL) methods such as the Deep Q-Network (DQN) have achieved state-of-the-art results in a variety of challenging, high-dimensional domains. This success is mainly attributed to the power of deep neural networks to learn rich domain representations for approximating the value function or policy. Batch reinforcement learning methods with linear representations, on the other hand, are more stable and require less hyper parameter tuning. Yet, substantial feature engineering is necessary to achieve good results. In this work we propose a hybrid approach -- the Least Squares Deep Q-Network (LS-DQN), which combines rich feature representations learned by a DRL algorithm with the stability of a linear least squares method. We do this by periodically re-training the last hidden layer of a DRL network with a batch least squares update. Key to our approach is a Bayesian regularization term for the least squares update, which prevents over-fitting to the more recent data. We tested LS-DQN on five Atari games and demonstrate significant improvement over vanilla DQN and Double-DQN. We also investigated the reasons for the superior performance of our method. Interestingly, we found that the performance improvement can be attributed to the large batch size used by the LS method when optimizing the last layer.

cs.AI↗

arXiv2017

A nonparametric sequential test for online randomized experiments

We propose a nonparametric sequential test that aims to address two practical problems pertinent to online randomized experiments: (i) how to do a hypothesis test for complex metrics; (ii) how to prevent type $1$ error inflation under continuous monitoring. The proposed test does not require knowledge of the underlying probability distribution generating the data. We use the bootstrap to estimate the likelihood for blocks of data followed by mixture sequential probability ratio test. We validate this procedure on data from a major online e-commerce website. We show that the proposed test controls type $1$ error at any time, has good power, is robust to misspecification in the distribution generating the data, and allows quick inference in online randomized experiments.

stat.ML↗

arXiv2017

Multi-objective Bandits: Optimizing the Generalized Gini Index

We study the multi-armed bandit (MAB) problem where the agent receives a vectorial feedback that encodes many possibly competing objectives to be optimized. The goal of the agent is to find a policy, which can optimize these objectives simultaneously in a fair way. This multi-objective online optimization problem is formalized by using the Generalized Gini Index (GGI) aggregation function. We propose an online gradient descent algorithm which exploits the convexity of the GGI aggregation function, and controls the exploration in a careful way achieving a distribution-free regret $\tilde{\bigO} (T^{-1/2} )$ with high probability. We test our algorithm on synthetic data as well as on an electric battery control problem where the goal is to trade off the use of the different cells of a battery in order to balance their respective degradation rates.

cs.LG↗

arXiv2017

Graying the black box: Understanding DQNs

In recent years there is a growing interest in using deep representations for reinforcement learning. In this paper, we present a methodology and tools to analyze Deep Q-networks (DQNs) in a non-blind matter. Moreover, we propose a new model, the Semi Aggregated Markov Decision Process (SAMDP), and an algorithm that learns it automatically. The SAMDP model allows us to identify spatio-temporal abstractions directly from features and may be used as a sub-goal detector in future work. Using our tools we reveal that the features learned by DQNs aggregate the state space in a hierarchical fashion, explaining its success. Moreover, we are able to understand and describe the policies learned by DQNs for three different Atari2600 games and suggest ways to interpret, debug and optimize deep neural networks in reinforcement learning.

cs.LG↗

arXiv2017

Deep Robust Kalman Filter

A Robust Markov Decision Process (RMDP) is a sequential decision making model that accounts for uncertainty in the parameters of dynamic systems. This uncertainty introduces difficulties in learning an optimal policy, especially for environments with large state spaces. We propose two algorithms, RTD-DQN and Deep-RoK, for solving large-scale RMDPs using nonlinear approximation schemes such as deep neural networks. The RTD-DQN algorithm incorporates the robust Bellman temporal difference error into a robust loss function, yielding robust policies for the agent. The Deep-RoK algorithm is a robust Bayesian method, based on the Extended Kalman Filter (EKF), that accounts for both the uncertainty in the weights of the approximated value function and the uncertainty in the transition probabilities, improving the robustness of the agent. We provide theoretical results for our approach and test the proposed algorithms on a continuous state domain.

cs.AI↗

arXiv2017

Online Learning with Many Experts

We study the problem of prediction with expert advice when the number of experts in question may be extremely large or even infinite. We devise an algorithm that obtains a tight regret bound of $\widetilde{O}(εT + N + \sqrt{NT})$, where $N$ is the empirical $ε$-covering number of the sequence of loss functions generated by the environment. In addition, we present a hedging procedure that allows us to find the optimal $ε$ in hindsight. Finally, we discuss a few interesting applications of our algorithm. We show how our algorithm is applicable in the approximately low rank experts model of Hazan et al. (2016), and discuss the case of experts with bounded variation, in which there is a surprisingly large gap between the regret bounds obtained in the statistical and online settings.

cs.LG↗

arXiv2017

Consistent On-Line Off-Policy Evaluation

The problem of on-line off-policy evaluation (OPE) has been actively studied in the last decade due to its importance both as a stand-alone problem and as a module in a policy improvement scheme. However, most Temporal Difference (TD) based solutions ignore the discrepancy between the stationary distribution of the behavior and target policies and its effect on the convergence limit when function approximation is applied. In this paper we propose the Consistent Off-Policy Temporal Difference (COP-TD($λ$, $β$)) algorithm that addresses this issue and reduces this bias at some computational expense. We show that COP-TD($λ$, $β$) can be designed to converge to the same value that would have been obtained by using on-policy TD($λ$) with the target policy. Subsequently, the proposed scheme leads to a related and promising heuristic we call log-COP-TD($λ$, $β$). Both algorithms have favorable empirical results to the current state of the art on-line OPE algorithms. Finally, our formulation sheds some new light on the recently proposed Emphatic TD learning.

stat.ML↗

arXiv2017

Outlier Robust Online Learning

We consider the problem of learning from noisy data in practical settings where the size of data is too large to store on a single machine. More challenging, the data coming from the wild may contain malicious outliers. To address the scalability and robustness issues, we present an online robust learning (ORL) approach. ORL is simple to implement and has provable robustness guarantee -- in stark contrast to existing online learning approaches that are generally fragile to outliers. We specialize the ORL approach for two concrete cases: online robust principal component analysis and online linear regression. We demonstrate the efficiency and robustness advantages of ORL through comprehensive simulations and predicting image tags on a large-scale data set. We also discuss extension of the ORL to distributed learning and provide experimental evaluations.

cs.LG↗

arXiv2016

Adaptive Lambda Least-Squares Temporal Difference Learning

Temporal Difference learning or TD($λ$) is a fundamental algorithm in the field of reinforcement learning. However, setting TD's $λ$ parameter, which controls the timescale of TD updates, is generally left up to the practitioner. We formalize the $λ$ selection problem as a bias-variance trade-off where the solution is the value of $λ$ that leads to the smallest Mean Squared Value Error (MSVE). To solve this trade-off we suggest applying Leave-One-Trajectory-Out Cross-Validation (LOTO-CV) to search the space of $λ$ values. Unfortunately, this approach is too computationally expensive for most practical applications. For Least Squares TD (LSTD) we show that LOTO-CV can be implemented efficiently to automatically tune $λ$ and apply function optimization methods to efficiently search the space of $λ$ values. The resulting algorithm, ALLSTD, is parameter free and our experiments demonstrate that ALLSTD is significantly computationally faster than the naïve LOTO-CV implementation while achieving similar performance.

cs.LG↗

arXiv2016

Supervised Learning for Optimal Power Flow as a Real-Time Proxy

In this work we design and compare different supervised learning algorithms to compute the cost of Alternating Current Optimal Power Flow (ACOPF). The motivation for quick calculation of OPF cost outcomes stems from the growing need of algorithmic-based long-term and medium-term planning methodologies in power networks. Integrated in a multiple time-horizon coordination framework, we refer to this approximation module as a proxy for predicting short-term decision outcomes without the need of actual simulation and optimization of them. Our method enables fast approximate calculation of OPF cost with less than 1% error on average, achieved in run-times that are several orders of magnitude lower than of exact computation. Several test-cases such as IEEE-RTS96 are used to demonstrate the efficiency of our approach.

cs.LG↗

arXiv2016

Model-based Adversarial Imitation Learning

Generative adversarial learning is a popular new approach to training generative models which has been proven successful for other related problems as well. The general idea is to maintain an oracle $D$ that discriminates between the expert's data distribution and that of the generative model $G$. The generative model is trained to capture the expert's distribution by maximizing the probability of $D$ misclassifying the data it generates. Overall, the system is \emph{differentiable} end-to-end and is trained using basic backpropagation. This type of learning was successfully applied to the problem of policy imitation in a model-free setup. However, a model-free approach does not allow the system to be differentiable, which requires the use of high-variance gradient estimations. In this paper we introduce the Model based Adversarial Imitation Learning (MAIL) algorithm. A model-based approach for the problem of adversarial imitation learning. We show how to use a forward model to make the system fully differentiable, which enables us to train policies using the (stochastic) gradient of $D$. Moreover, our approach requires relatively few environment interactions, and fewer hyper-parameters to tune. We test our method on the MuJoCo physics simulator and report initial results that surpass the current state-of-the-art.

stat.ML↗

arXiv2016

A Deep Hierarchical Approach to Lifelong Learning in Minecraft

We propose a lifelong learning system that has the ability to reuse and transfer knowledge from one task to another while efficiently retaining the previously learned knowledge-base. Knowledge is transferred by learning reusable skills to solve tasks in Minecraft, a popular video game which is an unsolved and high-dimensional lifelong learning problem. These reusable skills, which we refer to as Deep Skill Networks, are then incorporated into our novel Hierarchical Deep Reinforcement Learning Network (H-DRLN) architecture using two techniques: (1) a deep skill array and (2) skill distillation, our novel variation of policy distillation (Rusu et. al. 2015) for learning skills. Skill distillation enables the HDRLN to efficiently retain knowledge and therefore scale in lifelong learning, by accumulating knowledge and encapsulating multiple reusable skills into a single distilled network. The H-DRLN exhibits superior performance and lower learning sample complexity compared to the regular Deep Q Network (Mnih et. al. 2015) in sub-domains of Minecraft.

cs.AI↗

arXiv2016

Is a picture worth a thousand words? A Deep Multi-Modal Fusion Architecture for Product Classification in e-commerce

Classifying products into categories precisely and efficiently is a major challenge in modern e-commerce. The high traffic of new products uploaded daily and the dynamic nature of the categories raise the need for machine learning models that can reduce the cost and time of human editors. In this paper, we propose a decision level fusion approach for multi-modal product classification using text and image inputs. We train input specific state-of-the-art deep neural networks for each input source, show the potential of forging them together into a multi-modal architecture and train a novel policy network that learns to choose between them. Finally, we demonstrate that our multi-modal network improves the top-1 accuracy % over both networks on a real-world large-scale product classification dataset that we collected fromWalmart.com. While we focus on image-text fusion that characterizes e-commerce domains, our algorithms can be easily applied to other modalities such as audio, video, physical sensors, etc.

cs.CV↗

arXiv2016

Situational Awareness by Risk-Conscious Skills

Hierarchical Reinforcement Learning has been previously shown to speed up the convergence rate of RL planning algorithms as well as mitigate feature-based model misspecification (Mankowitz et. al. 2016a,b, Bacon 2015). To do so, it utilizes hierarchical abstractions, also known as skills -- a type of temporally extended action (Sutton et. al. 1999) to plan at a higher level, abstracting away from the lower-level details. We incorporate risk sensitivity, also referred to as Situational Awareness (SA), into hierarchical RL for the first time by defining and learning risk aware skills in a Probabilistic Goal Semi-Markov Decision Process (PG-SMDP). This is achieved using our novel Situational Awareness by Risk-Conscious Skills (SARiCoS) algorithm which comes with a theoretical convergence guarantee. We show in a RoboCup soccer domain that the learned risk aware skills exhibit complex human behaviors such as `time-wasting' in a soccer game. In addition, the learned risk aware skills are able to mitigate reward-based model misspecification.

cs.AI↗

arXiv2016

Clustering Time Series and the Surprising Robustness of HMMs

Suppose that we are given a time series where consecutive samples are believed to come from a probabilistic source, that the source changes from time to time and that the total number of sources is fixed. Our objective is to estimate the distributions of the sources. A standard approach to this problem is to model the data as a hidden Markov model (HMM). However, since the data often lacks the Markov or the stationarity properties of an HMM, one can ask whether this approach is still suitable or perhaps another approach is required. In this paper we show that a maximum likelihood HMM estimator can be used to approximate the source distributions in a much larger class of models than HMMs. Specifically, we propose a natural and fairly general non-stationary model of the data, where the only restriction is that the sources do not change too often. Our main result shows that for this model, a maximum-likelihood HMM estimator produces the correct second moment of the data, and the results can be extended to higher moments.

cs.IT↗