arXiv subjects

Shie Mannor

Publications and source records attributed to Shie Mannor.

At least 235 records · Page 13Linked to original sources

arXiv2013

Thompson Sampling for Complex Bandit Problems

We consider stochastic multi-armed bandit problems with complex actions over a set of basic arms, where the decision maker plays a complex action rather than a basic arm in each round. The reward of the complex action is some function of the basic arms' rewards, and the feedback observed may not necessarily be the reward per-arm. For instance, when the complex actions are subsets of the arms, we may only observe the maximum reward over the chosen subset. Thus, feedback across complex actions may be coupled due to the nature of the reward function. We prove a frequentist regret bound for Thompson sampling in a very general setting involving parameter, action and observation spaces and a likelihood function over them. The bound holds for discretely-supported priors over the parameter space and without additional structural properties such as closed-form posteriors, conjugate prior structure or independence across arms. The regret bound scales logarithmically with time but, more importantly, with an improved constant that non-trivially captures the coupling across complex actions due to the structure of the rewards. As applications, we derive improved regret bounds for classes of complex bandit problems involving selecting subsets of arms, including the first nontrivial regret bounds for nonlinear MAX reward feedback from subsets.

stat.ML↗

arXiv2013

Variance Adjusted Actor Critic Algorithms

We present an actor-critic framework for MDPs where the objective is the variance-adjusted expected return. Our critic uses linear function approximation, and we extend the concept of compatible features to the variance-adjusted setting. We present an episodic actor-critic algorithm and show that it converges almost surely to a locally optimal point of the objective function.

stat.ML↗

arXiv2013

Distinguishing Infections on Different Graph Topologies

The history of infections and epidemics holds famous examples where understanding, containing and ultimately treating an outbreak began with understanding its mode of spread. Influenza, HIV and most computer viruses, spread person to person, device to device, through contact networks; Cholera, Cancer, and seasonal allergies, on the other hand, do not. In this paper we study two fundamental questions of detection: first, given a snapshot view of a (perhaps vanishingly small) fraction of those infected, under what conditions is an epidemic spreading via contact (e.g., Influenza), distinguishable from a "random illness" operating independently of any contact network (e.g., seasonal allergies); second, if we do have an epidemic, under what conditions is it possible to determine which network of interactions is the main cause of the spread -- the causative network -- without any knowledge of the epidemic, other than the identity of a minuscule subsample of infected nodes? The core, therefore, of this paper, is to obtain an understanding of the diagnostic power of network information. We derive sufficient conditions networks must satisfy for these problems to be identifiable, and produce efficient, highly scalable algorithms that solve these problems. We show that the identifiability condition we give is fairly mild, and in particular, is satisfied by two common graph topologies: the grid, and the Erdos-Renyi graphs.

cs.SI↗

arXiv2013

Scaling Up Robust MDPs by Reinforcement Learning

We consider large-scale Markov decision processes (MDPs) with parameter uncertainty, under the robust MDP paradigm. Previous studies showed that robust MDPs, based on a minimax approach to handle uncertainty, can be solved using dynamic programming for small to medium sized problems. However, due to the "curse of dimensionality", MDPs that model real-life problems are typically prohibitively large for such approaches. In this work we employ a reinforcement learning approach to tackle this planning problem: we develop a robust approximate dynamic programming method based on a projected fixed point equation to approximately solve large scale robust MDPs. We show that the proposed method provably succeeds under certain technical conditions, and demonstrate its effectiveness through simulation of an option pricing problem. To the best of our knowledge, this is the first attempt to scale up the robust MDPs paradigm.

cs.LG↗

arXiv2013

A Primal Condition for Approachability with Partial Monitoring

In approachability with full monitoring there are two types of conditions that are known to be equivalent for convex sets: a primal and a dual condition. The primal one is of the form: a set C is approachable if and only all containing half-spaces are approachable in the one-shot game; while the dual one is of the form: a convex set C is approachable if and only if it intersects all payoff sets of a certain form. We consider approachability in games with partial monitoring. In previous works (Perchet 2011; Mannor et al. 2011) we provided a dual characterization of approachable convex sets; we also exhibited efficient strategies in the case where C is a polytope. In this paper we provide primal conditions on a convex set to be approachable with partial monitoring. They depend on a modified reward function and lead to approachability strategies, based on modified payoff functions, that proceed by projections similarly to Blackwell's (1956) strategy; this is in contrast with previously studied strategies in this context that relied mostly on the signaling structure and aimed at estimating well the distributions of the signals received. Our results generalize classical results by Kohlberg 1975 (see also Mertens et al. 1994) and apply to games with arbitrary signaling structure as well as to arbitrary convex sets.

math.OC↗

arXiv2013

Online Learning for Time Series Prediction

In this paper we address the problem of predicting a time series using the ARMA (autoregressive moving average) model, under minimal assumptions on the noise terms. Using regret minimization techniques, we develop effective online learning algorithms for the prediction problem, without assuming that the noise terms are Gaussian, identically distributed or even independent. Furthermore, we show that our algorithm's performances asymptotically approaches the performance of the best ARMA model in hindsight.

cs.LG↗

arXiv2013

Robust High Dimensional Sparse Regression and Matching Pursuit

We consider high dimensional sparse regression, and develop strategies able to deal with arbitrary -- possibly, severe or coordinated -- errors in the covariance matrix $X$. These may come from corrupted data, persistent experimental errors, or malicious respondents in surveys/recommender systems, etc. Such non-stochastic error-in-variables problems are notoriously difficult to treat, and as we demonstrate, the problem is particularly pronounced in high-dimensional settings where the primary goal is {\em support recovery} of the sparse regressor. We develop algorithms for support recovery in sparse regression, when some number $n_1$ out of $n+n_1$ total covariate/response pairs are {\it arbitrarily (possibly maliciously) corrupted}. We are interested in understanding how many outliers, $n_1$, we can tolerate, while identifying the correct support. To the best of our knowledge, neither standard outlier rejection techniques, nor recently developed robust regression algorithms (that focus only on corrupted response variables), nor recent algorithms for dealing with stochastic noise or erasures, can provide guarantees on support recovery. Perhaps surprisingly, we also show that the natural brute force algorithm that searches over all subsets of $n$ covariate/response pairs, and all subsets of possible support coordinates in order to minimize regression error, is remarkably poor, unable to correctly identify the support with even $n_1 = O(n/k)$ corrupted points, where $k$ is the sparsity. This is true even in the basic setting we consider, where all authentic measurements and noise are independent and sub-Gaussian. In this setting, we provide a simple algorithm -- no more computationally taxing than OMP -- that gives stronger performance guarantees, recovering the support with up to $n_1 = O(n/(\sqrt{k} \log p))$ corrupted points, where $p$ is the dimension of the signal to be recovered.

stat.ML↗

arXiv2013

Go Viral, or Not: Rate-Optimal Control for Resource-Constrained Branching Processes

We propose and analyze a new class of controlled multi-type branching processes with a per-step linear resource constraint, motivated by potential applications in viral marketing and cancer treatment. We show that the optimal exponential growth rate of the population can be achieved by maintaining a fixed proportion among the species, for both deterministic and stochastic branching processes. In the special case of a two-type population and with a symmetric reward structure, the optimal proportion is obtained in closed-form. In addition to revealing structural properties of controlled branching processes, our results are intended to provide the practitioners with an easy-to-interpret benchmark for best practices, if not exact policies. As a proof of concept, the methodology is applied to the linkage structure of the 2004 US Presidential Election blogosphere, where the optimal growth rate demonstrates sizable gains over a uniform selection strategy, and to a two-compartment cell-cycle kinetics model for cancer growth, with realistic parameters, where the robust estimate for minimal treatment intensity under a worst-case growth rate is noticeably more conservative compared to that obtained using more optimistic assumptions.

math.OC↗

arXiv2013

Policy Evaluation with Variance Related Risk Criteria in Markov Decision Processes

In this paper we extend temporal difference policy evaluation algorithms to performance criteria that include the variance of the cumulative reward. Such criteria are useful for risk management, and are important in domains such as finance and process control. We propose both TD(0) and LSTD(lambda) variants with linear function approximation, prove their convergence, and demonstrate their utility in a 4-dimensional continuous state space problem.

cs.LG↗

arXiv2012

The Perturbed Variation

We introduce a new discrepancy score between two distributions that gives an indication on their similarity. While much research has been done to determine if two samples come from exactly the same distribution, much less research considered the problem of determining if two finite samples come from similar distributions. The new score gives an intuitive interpretation of similarity; it optimally perturbs the distributions so that they best fit each other. The score is defined between distributions, and can be efficiently estimated from samples. We provide convergence bounds of the estimated score, and develop hypothesis testing procedures that test if two data sets come from similar distributions. The statistical power of this procedures is presented in simulations. We also compare the score's capacity to detect similarity with that of other known measures on real data.

cs.LG↗

arXiv2012

More Is Better: Large Scale Partially-supervised Sentiment Classification - Appendix

We describe a bootstrapping algorithm to learn from partially labeled data, and the results of an empirical study for using it to improve performance of sentiment classification using up to 15 million unlabeled Amazon product reviews. Our experiments cover semi-supervised learning, domain adaptation and weakly supervised learning. In some cases our methods were able to reduce test error by more than half using such large amount of data. NOTICE: This is only the supplementary material.

cs.LG↗

arXiv2012

How to sample if you must: on optimal functional sampling

We examine a fundamental problem that models various active sampling setups, such as network tomography. We analyze sampling of a multivariate normal distribution with an unknown expectation that needs to be estimated: in our setup it is possible to sample the distribution from a given set of linear functionals, and the difficulty addressed is how to optimally select the combinations to achieve low estimation error. Although this problem is in the heart of the field of optimal design, no efficient solutions for the case with many functionals exist. We present some bounds and an efficient sub-optimal solution for this problem for more structured sets such as binary functionals that are induced by graph walks.

stat.ML↗

arXiv2012

Decoupling Exploration and Exploitation in Multi-Armed Bandits

We consider a multi-armed bandit problem where the decision maker can explore and exploit different arms at every round. The exploited arm adds to the decision maker's cumulative reward (without necessarily observing the reward) while the explored arm reveals its value. We devise algorithms for this setup and show that the dependence on the number of arms, k, can be much better than the standard square root of k dependence, depending on the behavior of the arms' reward sequences. For the important case of piecewise stationary stochastic bandits, we show a significant improvement over existing algorithms. Our algorithms are based on a non-uniform sampling policy, which we show is essential to the success of any algorithm in the adversarial setup. Finally, we show some simulation results on an ultra-wide band channel selection inspired setting indicating the applicability of our algorithms.

cs.LG↗

arXiv2012

Policy Gradients with Variance Related Risk Criteria

Managing risk in dynamic decision problems is of cardinal importance in many fields such as finance and process control. The most common approach to defining risk is through various variance related criteria such as the Sharpe Ratio or the standard deviation adjusted reward. It is known that optimizing many of the variance related risk criteria is NP-hard. In this paper we devise a framework for local policy gradient style algorithms for reinforcement learning for variance related criteria. Our starting point is a new formula for the variance of the cost-to-go in episodic tasks. Using this formula we develop policy gradient algorithms for criteria that involve both the expected cost and the variance of the cost. We prove the convergence of these algorithms to local minima and demonstrate their applicability in a portfolio planning problem.

cs.LG↗

arXiv2012

Clustered Bandits

We consider a multi-armed bandit setting that is inspired by real-world applications in e-commerce. In our setting, there are a few types of users, each with a specific response to the different arms. When a user enters the system, his type is unknown to the decision maker. The decision maker can either treat each user separately ignoring the previously observed users, or can attempt to take advantage of knowing that only few types exist and cluster the users according to their response to the arms. We devise algorithms that combine the usual exploration-exploitation tradeoff with clustering of users and demonstrate the value of clustering. In the process of developing algorithms for the clustered setting, we propose and analyze simple algorithms for the setup where a decision maker knows that a user belongs to one of few types, but does not know which one.

cs.LG↗

arXiv2012

Lightning Does Not Strike Twice: Robust MDPs with Coupled Uncertainty

We consider Markov decision processes under parameter uncertainty. Previous studies all restrict to the case that uncertainties among different states are uncoupled, which leads to conservative solutions. In contrast, we introduce an intuitive concept, termed "Lightning Does not Strike Twice," to model coupled uncertain parameters. Specifically, we require that the system can deviate from its nominal parameters only a bounded number of times. We give probabilistic guarantees indicating that this model represents real life situations and devise tractable algorithms for computing optimal control policies using this concept.

cs.LG↗

arXiv2012

Relaxed Half-Stochastic Belief Propagation

Low-density parity-check codes are attractive for high throughput applications because of their low decoding complexity per bit, but also because all the codeword bits can be decoded in parallel. However, achieving this in a circuit implementation is complicated by the number of wires required to exchange messages between processing nodes. Decoding algorithms that exchange binary messages are interesting for fully-parallel implementations because they can reduce the number and the length of the wires, and increase logic density. This paper introduces the Relaxed Half-Stochastic (RHS) decoding algorithm, a binary message belief propagation (BP) algorithm that achieves a coding gain comparable to the best known BP algorithms that use real-valued messages. We derive the RHS algorithm by starting from the well-known Sum-Product algorithm, and then derive a low-complexity version suitable for circuit implementation. We present extensive simulation results on two standardized codes having different rates and constructions, including low bit error rate results. These simulations show that RHS can be an advantageous replacement for the existing state-of-the-art decoding algorithms when targeting fully-parallel implementations.

cs.AR↗

arXiv2012

Robust approachability and regret minimization in games with partial monitoring

Approachability has become a standard tool in analyzing earning algorithms in the adversarial online learning setup. We develop a variant of approachability for games where there is ambiguity in the obtained reward that belongs to a set, rather than being a single vector. Using this variant we tackle the problem of approachability in games with partial monitoring and develop simple and efficient algorithms (i.e., with constant per-step complexity) for this setup. We finally consider external regret and internal regret in repeated games with partial monitoring and derive regret-minimizing strategies based on approachability theory.

math.ST↗