arXiv subjects

Sanjay Shakkottai

Publications and source records attributed to Sanjay Shakkottai.

At least 73 records · Page 4Linked to original sources

arXiv2021

Contextual Bandits with Stochastic Experts

We consider the problem of contextual bandits with stochastic experts, which is a variation of the traditional stochastic contextual bandit with experts problem. In our problem setting, we assume access to a class of stochastic experts, where each expert is a conditional distribution over the arms given a context. We propose upper-confidence bound (UCB) algorithms for this problem, which employ two different importance sampling based estimators for the mean reward for each expert. Both these estimators leverage information leakage among the experts, thus using samples collected under all the experts to estimate the mean reward of any given expert. This leads to instance dependent regret bounds of $\mathcal{O}\left(λ(\pmbμ)\mathcal{M}\log T/Δ\right)$, where $λ(\pmbμ)$ is a term that depends on the mean rewards of the experts, $Δ$ is the smallest gap between the mean reward of the optimal expert and the rest, and $\mathcal{M}$ quantifies the information leakage among the experts. We show that under some assumptions $λ(\pmbμ)$ is typically $\mathcal{O}(\log N)$, where $N$ is the number of experts. We implement our algorithm with stochastic experts generated from cost-sensitive classification oracles and show superior empirical performance on real-world datasets, when compared to other state of the art contextual bandit algorithms.

stat.ML↗

arXiv2021

Stochastic Linear Bandits with Protected Subspace

We study a variant of the stochastic linear bandit problem wherein we optimize a linear objective function but rewards are accrued only orthogonal to an unknown subspace (which we interpret as a \textit{protected space}) given only zero-order stochastic oracle access to both the objective itself and protected subspace. In particular, at each round, the learner must choose whether to query the objective or the protected subspace alongside choosing an action. Our algorithm, derived from the OFUL principle, uses some of the queries to get an estimate of the protected space, and (in almost all rounds) plays optimistically with respect to a confidence set for this space. We provide a $\tilde{O}(sd\sqrt{T})$ regret upper bound in the case where the action space is the complete unit ball in $\mathbb{R}^d$, $s < d$ is the dimension of the protected subspace, and $T$ is the time horizon. Moreover, we demonstrate that a discrete action space can lead to linear regret with an optimistic algorithm, reinforcing the sub-optimality of optimism in certain settings. We also show that protection constraints imply that for certain settings, no consistent algorithm can have a regret smaller than $Ω(T^{3/4}).$ We finally empirically validate our results with synthetic and real datasets.

cs.LG↗

arXiv2020

Applications of Common Entropy for Causal Inference

We study the problem of discovering the simplest latent variable that can make two observed discrete variables conditionally independent. The minimum entropy required for such a latent is known as common entropy in information theory. We extend this notion to Renyi common entropy by minimizing the Renyi entropy of the latent variable. To efficiently compute common entropy, we propose an iterative algorithm that can be used to discover the trade-off between the entropy of the latent variable and the conditional mutual information of the observed variables. We show two applications of common entropy in causal inference: First, under the assumption that there are no low-entropy mediators, it can be used to distinguish causation from spurious correlation among almost all joint distributions on simple causal graphs with two observed variables. Second, common entropy can be used to improve constraint-based methods such as PC or FCI algorithms in the small-sample regime, where these methods are known to struggle. We propose a modification to these constraint-based methods to assess if a separating set found by these algorithms is valid using common entropy. We finally evaluate our algorithms on synthetic and real data to establish their performance.

stat.ML↗

arXiv2020

One-bit feedback is sufficient for upper confidence bound policies

We consider a variant of the traditional multi-armed bandit problem in which each arm is only able to provide one-bit feedback during each pull based on its past history of rewards. Our main result is the following: given an upper confidence bound policy which uses full-reward feedback, there exists a coding scheme for generating one-bit feedback, and a corresponding decoding scheme and arm selection policy, such that the ratio of the regret achieved by our policy and the regret of the full-reward feedback policy asymptotically approaches one.

cs.LG↗

arXiv2020

Verification and Parameter Synthesis for Stochastic Systems using Optimistic Optimization

We present an algorithm for formal verification and parameter synthesis of continuous state-space Markov chains. This class of problems captures the design and analysis of a wide variety of autonomous and cyber-physical systems defined by nonlinear and black-box modules. In order to solve these problems, one has to maximize certain probabilistic objective functions overall choices of initial states and parameters. In this paper, we identify the assumptions that make it possible to view this problem as a multi-armed bandit problem. Based on this fresh perspective, we propose an algorithm (HOO-MB) for solving the problem that carefully instantiates an existing bandit algorithm -- Hierarchical Optimistic Optimization -- with appropriate parameters. As a consequence, we obtain theoretical regret bounds on sample efficiency of our solution that depends on key problem parameters like smoothness, near-optimality dimension, and batch size. The batch size parameter enables us to strike a balance between the sample efficiency and the memory usage of the algorithm. Our experiments, using the tool HooVer, suggest that the approach scales to realistic-sized problems and is often more sample-efficient compared to PlasmaLab -- a leading tool for verification of stochastic systems. Specifically, HooVer has distinct advantages in analyzing models in which the objective function has sharp slopes. In addition, HooVer shows promising behavior in parameter synthesis for a linear quadratic regulator (LQR) example.

cs.LG↗

arXiv2020

Importance Weighted Generative Networks

Deep generative networks can simulate from a complex target distribution, by minimizing a loss with respect to samples from that distribution. However, often we do not have direct access to our target distribution - our data may be subject to sample selection bias, or may be from a different but related distribution. We present methods based on importance weighting that can estimate the loss with respect to a target distribution, even if we cannot access that distribution directly, in a variety of settings. These estimators, which differentially weight the contribution of data to the loss function, offer both theoretical guarantees and impressive empirical performance.

stat.ML↗

arXiv2020

Mix and Match: An Optimistic Tree-Search Approach for Learning Models from Mixture Distributions

We consider a covariate shift problem where one has access to several different training datasets for the same learning problem and a small validation set which possibly differs from all the individual training distributions. This covariate shift is caused, in part, due to unobserved features in the datasets. The objective, then, is to find the best mixture distribution over the training datasets (with only observed features) such that training a learning algorithm using this mixture has the best validation performance. Our proposed algorithm, ${\sf Mix\&Match}$, combines stochastic gradient descent (SGD) with optimistic tree search and model re-use (evolving partially trained models with samples from different mixture distributions) over the space of mixtures, for this task. We prove simple regret guarantees for our algorithm with respect to recovering the optimal mixture, given a total budget of SGD evaluations. Finally, we validate our algorithm on two real-world datasets.

stat.ML↗

arXiv2020

Task-Robust Model-Agnostic Meta-Learning

Meta-learning methods have shown an impressive ability to train models that rapidly learn new tasks. However, these methods only aim to perform well in expectation over tasks coming from some particular distribution that is typically equivalent across meta-training and meta-testing, rather than considering worst-case task performance. In this work we introduce the notion of "task-robustness" by reformulating the popular Model-Agnostic Meta-Learning (MAML) objective [Finn et al. 2017] such that the goal is to minimize the maximum loss over the observed meta-training tasks. The solution to this novel formulation is task-robust in the sense that it places equal importance on even the most difficult and/or rare tasks. This also means that it performs well over all distributions of the observed tasks, making it robust to shifts in the task distribution between meta-training and meta-testing. We present an algorithm to solve the proposed min-max problem, and show that it converges to an $ε$-accurate point at the optimal rate of $\mathcal{O}(1/ε^2)$ in the convex setting and to an $(ε, δ)$-stationary point at the rate of $\mathcal{O}(\max\{1/ε^5, 1/δ^5\})$ in nonconvex settings. We also provide an upper bound on the new task generalization error that captures the advantage of minimizing the worst-case task loss, and demonstrate this advantage in sinusoid regression and image classification experiments.

cs.LG↗

arXiv2020

Contextual Blocking Bandits

We study a novel variant of the multi-armed bandit problem, where at each time step, the player observes an independently sampled context that determines the arms' mean rewards. However, playing an arm blocks it (across all contexts) for a fixed and known number of future time steps. The above contextual setting, which captures important scenarios such as recommendation systems or ad placement with diverse users, invalidates greedy solution techniques that are effective for its non-contextual counterpart (Basu et al., NeurIPS19). Assuming knowledge of the context distribution and the mean reward of each arm-context pair, we cast the problem as an online bipartite matching problem, where the right-vertices (contexts) arrive stochastically and the left-vertices (arms) are blocked for a finite number of rounds each time they are matched. This problem has been recently studied in the full-information case, where competitive ratio bounds have been derived. We focus on the bandit setting, where the reward distributions are initially unknown; we propose a UCB-based variant of the full-information algorithm that guarantees a $\mathcal{O}(\log T)$-regret w.r.t. an $α$-optimal strategy in $T$ time steps, matching the $Ω(\log(T))$ regret lower bound in this setting. Due to the time correlations caused by blocking, existing techniques for upper bounding regret fail. For proving our regret bounds, we introduce the novel concepts of delayed exploitation and opportunistic subsampling and combine them with ideas from combinatorial bandits and non-stationary Markov chains coupling.

cs.LG↗

arXiv2019

Learning Unknown Service Rates in Queues: A Multi-Armed Bandit Approach

Consider a queueing system consisting of multiple servers. Jobs arrive over time and enter a queue for service; the goal is to minimize the size of this queue. At each opportunity for service, at most one server can be chosen, and at most one job can be served. Service is successful with a probability (the service probability) that is a priori unknown for each server. An algorithm that knows the service probabilities (the "genie") can always choose the server of highest service probability. We study algorithms that learn the unknown service probabilities. Our goal is to minimize queue-regret: the (expected) difference between the queue-lengths obtained by the algorithm, and those obtained by the "genie." Since queue-regret cannot be larger than classical regret, results for the standard multi-armed bandit problem give algorithms for which queue-regret increases no more than logarithmically in time. Our paper shows surprisingly more complex behavior. In particular, as long as the bandit algorithm's queues have relatively long regenerative cycles, queue-regret is similar to cumulative regret, and scales (essentially) logarithmically. However, we show that this "early stage" of the queueing bandit eventually gives way to a "late stage", where the optimal queue-regret scaling is $O(1/t)$. We demonstrate an algorithm that (order-wise) achieves this asymptotic queue-regret in the late stage. Our results are developed in a more general model that allows for multiple job classes as well.

eess.SY↗

arXiv2019

Social Learning in Multi Agent Multi Armed Bandits

In this paper, we introduce a distributed version of the classical stochastic Multi-Arm Bandit (MAB) problem. Our setting consists of a large number of agents $n$ that collaboratively and simultaneously solve the same instance of $K$ armed MAB to minimize the average cumulative regret over all agents. The agents can communicate and collaborate among each other \emph{only} through a pairwise asynchronous gossip based protocol that exchange a limited number of bits. In our model, agents at each point decide on (i) which arm to play, (ii) whether to, and if so (iii) what and whom to communicate with. Agents in our model are decentralized, namely their actions only depend on their observed history in the past. We develop a novel algorithm in which agents, whenever they choose, communicate only arm-ids and not samples, with another agent chosen uniformly and independently at random. The per-agent regret scaling achieved by our algorithm is $O \left( \frac{\lceil\frac{K}{n}\rceil+\log(n)}Δ \log(T) + \frac{\log^3(n) \log \log(n)}{Δ^2} \right)$. Furthermore, any agent in our algorithm communicates only a total of $Θ(\log(T))$ times over a time interval of $T$. We compare our results to two benchmarks - one where there is no communication among agents and one corresponding to complete interaction. We show both theoretically and empirically, that our algorithm experiences a significant reduction both in per-agent regret when compared to the case when agents do not collaborate and in communication complexity when compared to the full interaction setting which requires $T$ communication attempts by an agent over $T$ arm pulls.

cs.LG↗

arXiv2018

Noisy Blackbox Optimization with Multi-Fidelity Queries: A Tree Search Approach

We study the problem of black-box optimization of a noisy function in the presence of low-cost approximations or fidelities, which is motivated by problems like hyper-parameter tuning. In hyper-parameter tuning evaluating the black-box function at a point involves training a learning algorithm on a large data-set at a particular hyper-parameter and evaluating the validation error. Even a single such evaluation can be prohibitively expensive. Therefore, it is beneficial to use low-cost approximations, like training the learning algorithm on a sub-sampled version of the whole data-set. These low-cost approximations/fidelities can however provide a biased and noisy estimate of the function value. In this work, we incorporate the multi-fidelity setup in the powerful framework of noisy black-box optimization through tree-like hierarchical partitions. We propose a multi-fidelity bandit based tree-search algorithm for the problem and provide simple regret bounds for our algorithm. Finally, we validate the performance of our algorithm on real and synthetic datasets, where it outperforms several benchmarks.

stat.ML↗

arXiv2018

Joint Scheduling of URLLC and eMBB Traffic in 5G Wireless Networks

Emerging 5G systems will need to efficiently support both enhanced mobile broadband traffic (eMBB) and ultra-low-latency communications (URLLC) traffic. In these systems, time is divided into slots which are further sub-divided into minislots. From a scheduling perspective, eMBB resource allocations occur at slot boundaries, whereas to reduce latency URLLC traffic is pre-emptively overlapped at the minislot timescale, resulting in selective superposition/puncturing of eMBB allocations. This approach enables minimal URLLC latency at a potential rate loss to eMBB traffic. We study joint eMBB and URLLC schedulers for such systems, with the dual objectives of maximizing utility for eMBB traffic while immediately satisfying URLLC demands. For a linear rate loss model (loss to eMBB is linear in the amount of URLLC superposition/puncturing), we derive an optimal joint scheduler. Somewhat counter-intuitively, our results show that our dual objectives can be met by an iterative gradient scheduler for eMBB traffic that anticipates the expected loss from URLLC traffic, along with an URLLC demand scheduler that is oblivious to eMBB channel states, utility functions and allocation decisions of the eMBB scheduler. Next we consider a more general class of (convex/threshold) loss models and study optimal online joint eMBB/URLLC schedulers within the broad class of channel state dependent but minislot-homogeneous policies. A key observation is that unlike the linear rate loss model, for the convex and threshold rate loss models, optimal eMBB and URLLC scheduling decisions do not de-couple and joint optimization is necessary to satisfy the dual objectives. We validate the characteristics and benefits of our schedulers via simulation.

cs.NI↗

arXiv2018

Augmenting Max-Weight with Explicit Learning for Wireless Scheduling with Switching Costs

In small-cell wireless networks where users are connected to multiple base stations (BSs), it is often advantageous to switch off dynamically a subset of BSs to minimize energy costs. We consider two types of energy cost: (i) the cost of maintaining a BS in the active state, and (ii) the cost of switching a BS from the active state to inactive state. The problem is to operate the network at the lowest possible energy cost (sum of activation and switching costs) subject to queue stability. In this setting, the traditional approach -- a Max-Weight algorithm along with a Lyapunov-based stability argument -- does not suffice to show queue stability, essentially due to the temporal co-evolution between channel scheduling and the BS activation decisions induced by the switching cost. Instead, we develop a learning and BS activation algorithm with slow temporal dynamics, and a Max-Weight based channel scheduler that has fast temporal dynamics. We show using convergence of time-inhomogeneous Markov chains, that the co-evolving dynamics of learning, BS activation and queue lengths lead to near optimal average energy costs along with queue stability.

eess.SY↗

arXiv2018

On Learning the $cμ$ Rule in Single and Parallel Server Networks

We consider learning-based variants of the $c μ$ rule for scheduling in single and parallel server settings of multi-class queueing systems. In the single server setting, the $c μ$ rule is known to minimize the expected holding-cost (weighted queue-lengths summed over classes and a fixed time horizon). We focus on the problem where the service rates $μ$ are unknown with the holding-cost regret (regret against the $c μ$ rule with known $μ$) as our objective. We show that the greedy algorithm that uses empirically learned service rates results in a constant holding-cost regret (the regret is independent of the time horizon). This free exploration can be explained in the single server setting by the fact that any work-conserving policy obtains the same number of samples in a busy cycle. In the parallel server setting, we show that the $c μ$ rule may result in unstable queues, even for arrival rates within the capacity region. We then present sufficient conditions for geometric ergodicity under the $c μ$ rule. Using these results, we propose an almost greedy algorithm that explores only when the number of samples falls below a threshold. We show that this algorithm delivers constant holding-cost regret because a free exploration condition is eventually satisfied.

cs.PF↗

arXiv2018

Searching for a Single Community in a Graph

In standard graph clustering/community detection, one is interested in partitioning the graph into more densely connected subsets of nodes. In contrast, the "search" problem of this paper aims to only find the nodes in a "single" such community, the target, out of the many communities that may exist. To do so , we are given suitable side information about the target; for example, a very small number of nodes from the target are labeled as such. We consider a general yet simple notion of side information: all nodes are assumed to have random weights, with nodes in the target having higher weights on average. Given these weights and the graph, we develop a variant of the method of moments that identifies nodes in the target more reliably, and with lower computation, than generic community detection methods that do not use side information and partition the entire graph. Our empirical results show significant gains in runtime, and also gains in accuracy over other graph clustering algorithms.

cs.SI↗

arXiv2018

The Shape of Alerts: Detecting Malware Using Distributed Detectors by Robustly Amplifying Transient Correlations

We introduce a new malware detector - Shape-GD - that aggregates per-machine detectors into a robust global detector. Shape-GD is based on two insights: 1. Structural: actions such as visiting a website (waterhole attack) by nodes correlate well with malware spread, and create dynamic neighborhoods of nodes that were exposed to the same attack vector. However, neighborhood sizes vary unpredictably and require aggregating an unpredictable number of local detectors' outputs into a global alert. 2. Statistical: feature vectors corresponding to true and false positives of local detectors have markedly different conditional distributions - i.e. their shapes differ. The shape of neighborhoods can identify infected neighborhoods without having to estimate neighborhood sizes - on 5 years of Symantec detectors' logs, Shape-GD reduces false positives from ~1M down to ~110K and raises alerts 345 days (on average) before commercial anti-virus products; in a waterhole attack simulated using Yahoo web-service logs, Shape-GD detects infected machines when only ~100 of ~550K are compromised.

cs.CR↗

arXiv2018

The Search Problem in Mixture Models

We consider the task of learning the parameters of a {\em single} component of a mixture model, for the case when we are given {\em side information} about that component, we call this the "search problem" in mixture models. We would like to solve this with computational and sample complexity lower than solving the overall original problem, where one learns parameters of all components. Our main contributions are the development of a simple but general model for the notion of side information, and a corresponding simple matrix-based algorithm for solving the search problem in this general setting. We then specialize this model and algorithm to four common scenarios: Gaussian mixture models, LDA topic models, subspace clustering, and mixed linear regression. For each one of these we show that if (and only if) the side information is informative, we obtain parameter estimates with greater accuracy, and also improved computation complexity than existing moment based mixture model algorithms (e.g. tensor methods). We also illustrate several natural ways one can obtain such side information, for specific problem instances. Our experiments on real data sets (NY Times, Yelp, BSDS500) further demonstrate the practicality of our algorithms showing significant improvement in runtime and accuracy.

stat.ML↗