arXiv subjects

Ioannis Ch. Paschalidis

Publications and source records attributed to Ioannis Ch. Paschalidis.

At least 55 records · Page 3Linked to original sources

arXiv2021

Generalized Proximal Policy Optimization with Sample Reuse

In real-world decision making tasks, it is critical for data-driven reinforcement learning methods to be both stable and sample efficient. On-policy methods typically generate reliable policy improvement throughout training, while off-policy methods make more efficient use of data through sample reuse. In this work, we combine the theoretically supported stability benefits of on-policy algorithms with the sample efficiency of off-policy algorithms. We develop policy improvement guarantees that are suitable for the off-policy setting, and connect these bounds to the clipping mechanism used in Proximal Policy Optimization. This motivates an off-policy version of the popular algorithm that we call Generalized Proximal Policy Optimization with Sample Reuse. We demonstrate both theoretically and empirically that our algorithm delivers improved performance by effectively balancing the competing goals of stability and sample efficiency.

cs.LG↗

arXiv2021

Communication-efficient SGD: From Local SGD to One-Shot Averaging

We consider speeding up stochastic gradient descent (SGD) by parallelizing it across multiple workers. We assume the same data set is shared among $N$ workers, who can take SGD steps and coordinate with a central server. While it is possible to obtain a linear reduction in the variance by averaging all the stochastic gradients at every step, this requires a lot of communication between the workers and the server, which can dramatically reduce the gains from parallelism. The Local SGD method, proposed and analyzed in the earlier literature, suggests machines should make many local steps between such communications. While the initial analysis of Local SGD showed it needs $Ω( \sqrt{T} )$ communications for $T$ local gradient steps in order for the error to scale proportionately to $1/(NT)$, this has been successively improved in a string of papers, with the state of the art requiring $Ω\left( N \left( \mbox{ poly} (\log T) \right) \right)$ communications. In this paper, we suggest a Local SGD scheme that communicates less overall by communicating less frequently as the number of iterations grows. Our analysis shows that this can achieve an error that scales as $1/(NT)$ with a number of communications that is completely independent of $T$. In particular, we show that $Ω(N)$ communications are sufficient. Empirical evidence suggests this bound is close to tight as we further show that $\sqrt{N}$ or $N^{3/4}$ communications fail to achieve linear speed-up in simulations. Moreover, we show that under mild assumptions, the main of which is twice differentiability on any neighborhood of the optimal solution, one-shot averaging which only uses a single round of communication can also achieve the optimal convergence rate asymptotically.

cs.DC↗

arXiv2021

Distributionally Robust Learning

This monograph develops a comprehensive statistical learning framework that is robust to (distributional) perturbations in the data using Distributionally Robust Optimization (DRO) under the Wasserstein metric. Beginning with fundamental properties of the Wasserstein metric and the DRO formulation, we explore duality to arrive at tractable formulations and develop finite-sample, as well as asymptotic, performance guarantees. We consider a series of learning problems, including (i) distributionally robust linear regression; (ii) distributionally robust regression with group structure in the predictors; (iii) distributionally robust multi-output regression and multiclass classification, (iv) optimal decision making that combines distributionally robust regression with nearest-neighbor estimation; (v) distributionally robust semi-supervised learning, and (vi) distributionally robust reinforcement learning. A tractable DRO relaxation for each problem is being derived, establishing a connection between robustness and regularization, and obtaining bounds on the prediction and estimation errors of the solution. Beyond theory, we include numerical experiments and case studies using synthetic and real data. The real data experiments are all associated with various health informatics problems, an application area which provided the initial impetus for this work.

stat.ML↗

arXiv2021

Planning Strategies for Lane Reversals in Transportation Networks

This paper studies strategies to optimize the lane configuration of a transportation network for a given set of Origin-Destination demands using a planning macroscopic network flow model. The lane reversal problem is, in general, NP-hard since the optimization is made over integer variables. To overcome this burden, we reformulate the problem using a piecewise affine approximation of the travel latency function which allows us to exploit the total unimodularity property of Integer Linear Programming (ILP). Consequently, we transform the ILP problem to a linear program by relaxing the integer variables. In addition, our method is capable of solving the problem for a desired number of lane reversals which serves to perform cost-benefit analysis. We perform a case study using the transportation network of Eastern Massachusetts (EMA) and we test our method against the original lane configuration and a projected lower bound solution. Our empirical results quantify the travel time savings for different levels of demand intensity. We observe reduction in travel times up to 40% for certain links in the network.

math.OC↗

arXiv2021

Online Baum-Welch algorithm for Hierarchical Imitation Learning

The options framework for hierarchical reinforcement learning has increased its popularity in recent years and has made improvements in tackling the scalability problem in reinforcement learning. Yet, most of these recent successes are linked with a proper options initialization or discovery. When an expert is available, the options discovery problem can be addressed by learning an options-type hierarchical policy directly from expert demonstrations. This problem is referred to as hierarchical imitation learning and can be handled as an inference problem in a Hidden Markov Model, which is done via an Expectation-Maximization type algorithm. In this work, we propose a novel online algorithm to perform hierarchical imitation learning in the options framework. Further, we discuss the benefits of such an algorithm and compare it with its batch version in classical reinforcement learning benchmarks. We show that this approach works well in both discrete and continuous environments and, under certain conditions, it outperforms the batch version.

cs.LG↗

arXiv2021

A Sharp Estimate on the Transient Time of Distributed Stochastic Gradient Descent

This paper is concerned with minimizing the average of $n$ cost functions over a network in which agents may communicate and exchange information with each other. We consider the setting where only noisy gradient information is available. To solve the problem, we study the distributed stochastic gradient descent (DSGD) method and perform a non-asymptotic convergence analysis. For strongly convex and smooth objective functions, DSGD asymptotically achieves the optimal network independent convergence rate compared to centralized stochastic gradient descent (SGD). Our main contribution is to characterize the transient time needed for DSGD to approach the asymptotic convergence rate, which we show behaves as $K_T=\mathcal{O}\left(\frac{n}{(1-ρ_w)^2}\right)$, where $1-ρ_w$ denotes the spectral gap of the mixing matrix. Moreover, we construct a "hard" optimization problem for which we show the transient time needed for DSGD to approach the asymptotic convergence rate is lower bounded by $Ω\left(\frac{n}{(1-ρ_w)^2} \right)$, implying the sharpness of the obtained result. Numerical experiments demonstrate the tightness of the theoretical results.

math.OC↗

arXiv2020

Uncertainty-Aware Policy Optimization: A Robust, Adaptive Trust Region Approach

In order for reinforcement learning techniques to be useful in real-world decision making processes, they must be able to produce robust performance from limited data. Deep policy optimization methods have achieved impressive results on complex tasks, but their real-world adoption remains limited because they often require significant amounts of data to succeed. When combined with small sample sizes, these methods can result in unstable learning due to their reliance on high-dimensional sample-based estimates. In this work, we develop techniques to control the uncertainty introduced by these estimates. We leverage these techniques to propose a deep policy optimization approach designed to produce stable performance even when data is scarce. The resulting algorithm, Uncertainty-Aware Trust Region Policy Optimization, generates robust policy updates that adapt to the level of uncertainty present throughout the learning process.

cs.LG↗

arXiv2020

Explainability of Intelligent Transportation Systems using Knowledge Compilation: a Traffic Light Controller Case

Usage of automated controllers which make decisions on an environment are widespread and are often based on black-box models. We use Knowledge Compilation theory to bring explainability to the controller's decision given the state of the system. For this, we use simulated historical state-action data as input and build a compact and structured representation which relates states with actions. We implement this method in a Traffic Light Control scenario where the controller selects the light cycle by observing the presence (or absence) of vehicles in different regions of the incoming roads.

cs.AI↗

arXiv2020

Robustified Multivariate Regression and Classification Using Distributionally Robust Optimization under the Wasserstein Metric

We develop Distributionally Robust Optimization (DRO) formulations for Multivariate Linear Regression (MLR) and Multiclass Logistic Regression (MLG) when both the covariates and responses/labels may be contaminated by outliers. The DRO framework uses a probabilistic ambiguity set defined as a ball of distributions that are close to the empirical distribution of the training set in the sense of the Wasserstein metric. We relax the DRO formulation into a regularized learning problem whose regularizer is a norm of the coefficient matrix. We establish out-of-sample performance guarantees for the solutions to our model, offering insights on the role of the regularizer in controlling the prediction error. Experimental results show that our approach improves the predictive error by 7% -- 37% for MLR, and a metric of robustness by 100% for MLG.

stat.ML↗

arXiv2020

Robust Grouped Variable Selection Using Distributionally Robust Optimization

We propose a Distributionally Robust Optimization (DRO) formulation with a Wasserstein-based uncertainty set for selecting grouped variables under perturbations on the data for both linear regression and classification problems. The resulting model offers robustness explanations for Grouped Least Absolute Shrinkage and Selection Operator (GLASSO) algorithms and highlights the connection between robustness and regularization. We prove probabilistic bounds on the out-of-sample loss and the estimation bias, and establish the grouping effect of our estimator, showing that coefficients in the same group converge to the same value as the sample correlation between covariates approaches 1. Based on this result, we propose to use the spectral clustering algorithm with the Gaussian similarity function to perform grouping on the predictors, which makes our approach applicable without knowing the grouping structure a priori. We compare our approach to an array of alternatives and provide extensive numerical results on both synthetic data and a real large dataset of surgery-related medical records, showing that our formulation produces an interpretable and parsimonious model that encourages sparsity at a group level and is able to achieve better prediction and estimation performance in the presence of outliers.

stat.ML↗

arXiv2020

Local SGD With a Communication Overhead Depending Only on the Number of Workers

We consider speeding up stochastic gradient descent (SGD) by parallelizing it across multiple workers. We assume the same data set is shared among $n$ workers, who can take SGD steps and coordinate with a central server. Unfortunately, this could require a lot of communication between the workers and the server, which can dramatically reduce the gains from parallelism. The Local SGD method, proposed and analyzed in the earlier literature, suggests machines should make many local steps between such communications. While the initial analysis of Local SGD showed it needs $Ω( \sqrt{T} )$ communications for $T$ local gradient steps in order for the error to scale proportionately to $1/(nT)$, this has been successively improved in a string of papers, with the state-of-the-art requiring $Ω\left( n \left( \mbox{ polynomial in log } (T) \right) \right)$ communications. In this paper, we give a new analysis of Local SGD. A consequence of our analysis is that Local SGD can achieve an error that scales as $1/(nT)$ with only a fixed number of communications independent of $T$: specifically, only $Ω(n)$ communications are required.

math.OC↗

arXiv2020

Joint Pricing and Rebalancing of Autonomous Mobility-on-Demand Systems

This paper studies optimal pricing and rebalancing policies for Autonomous Mobility-on-Demand (AMoD) systems. We take a macroscopic planning perspective to tackle a profit maximization problem while ensuring that the system is load-balanced. We begin by describing the system using a dynamic fluid model to show the existence and stability of an equilibrium (i.e., load balance) through pricing policies. We then develop an optimization framework that allows us to find optimal policies in terms of pricing and rebalancing. We first maximize profit by only using pricing policies, then incorporate rebalancing, and finally we consider whether the solution is found sequentially or jointly. We apply each approach on a data-driven case study using real taxi data from New York City. Depending on which benchmarking solution we use, the joint problem (i.e., pricing and rebalancing) increases profits by 7% to 40%

math.OC↗

arXiv2020

Congestion-aware Routing and Rebalancing of Autonomous Mobility-on-Demand Systems in Mixed Traffic

This paper studies congestion-aware route-planning policies for Autonomous Mobility-on-Demand (AMoD) systems, whereby a fleet of autonomous vehicles provides on-demand mobility under mixed traffic conditions. Specifically, we first devise a network flow model to optimize the AMoD routing and rebalancing strategies in a congestion-aware fashion by accounting for the endogenous impact of AMoD flows on travel time. Second, we capture reactive exogenous traffic consisting of private vehicles selfishly adapting to the AMoD flows in a user-centric fashion by leveraging an iterative approach. Finally, we showcase the effectiveness of our framework with two case-studies considering the transportation sub-networks in Eastern Massachusetts and New York City. Our results suggest that for high levels of demand, pure AMoD travel can be detrimental due to the additional traffic stemming from its rebalancing flows, while the combination of AMoD with walking or micromobility options can significantly improve the overall system performance.

eess.SY↗

arXiv2020

Asymptotic Network Independence in Distributed Stochastic Optimization for Machine Learning

We provide a discussion of several recent results which, in certain scenarios, are able to overcome a barrier in distributed stochastic optimization for machine learning. Our focus is the so-called asymptotic network independence property, which is achieved whenever a distributed method executed over a network of n nodes asymptotically converges to the optimal solution at a comparable rate to a centralized method with the same computational power as the entire network. We explain this property through an example involving the training of ML models and sketch a short mathematical analysis for comparing the performance of distributed stochastic gradient descent (DSGD) with centralized stochastic gradient decent (SGD).

math.OC↗

arXiv2019

Robust Asynchronous Stochastic Gradient-Push: Asymptotically Optimal and Network-Independent Performance for Strongly Convex Functions

We consider the standard model of distributed optimization of a sum of functions $F(\bz) = \sum_{i=1}^n f_i(\bz)$, where node $i$ in a network holds the function $f_i(\bz)$. We allow for a harsh network model characterized by asynchronous updates, message delays, unpredictable message losses, and directed communication among nodes. In this setting, we analyze a modification of the Gradient-Push method for distributed optimization, assuming that \begin{enumerate*}[label=(\roman*)] \item node $i$ is capable of generating gradients of its function $f_i(\bz)$ corrupted by zero-mean bounded-support additive noise at each step, \item $F(\bz)$ is strongly convex, and \item each $f_i(\bz)$ has Lipschitz gradients. We show that our proposed method asymptotically performs as well as the best bounds on centralized gradient descent that takes steps in the direction of the sum of the noisy gradients of all the functions $f_1(\bz), \ldots, f_n(\bz)$ at each step.

math.OC↗

arXiv2019

Convergence of Parameter Estimates for Regularized Mixed Linear Regression Models

We consider {\em Mixed Linear Regression (MLR)}, where training data have been generated from a mixture of distinct linear models (or clusters) and we seek to identify the corresponding coefficient vectors. We introduce a {\em Mixed Integer Programming (MIP)} formulation for MLR subject to regularization constraints on the coefficient vectors. We establish that as the number of training samples grows large, the MIP solution converges to the true coefficient vectors in the absence of noise. Subject to slightly stronger assumptions, we also establish that the MIP identifies the clusters from which the training samples were generated. In the special case where training data come from a single cluster, we establish that the corresponding MIP yields a solution that converges to the true coefficient vector even when training data are perturbed by (martingale difference) noise. We provide a counterexample indicating that in the presence of noise, the MIP may fail to produce the true coefficient vectors for more than one clusters. We also provide numerical results testing the MIP solutions in synthetic examples with noise.

stat.ML↗

arXiv2019

Joint Estimation of OD Demands and Cost Functions in Transportation Networks from Data

Existing work has tackled the problem of estimating Origin-Destination (OD) demands and recovering travel latency functions in transportation networks under the Wardropian assumption. The ultimate objective is to derive an accurate predictive model of the network to enable optimization and control. However, these two problems are typically treated separately and estimation is based on parametric models. In this paper, we propose a method to jointly recover nonparametric travel latency cost functions and estimate OD demands using traffic flow data. We formulate the problem as a bilevel optimization problem and develop an iterative first-order optimization algorithm to solve it. A numerical example using the Braess Network is presented to demonstrate the effectiveness of our method.

math.OC↗

arXiv2019

Prescriptive Cluster-Dependent Support Vector Machines with an Application to Reducing Hospital Readmissions

We augment linear Support Vector Machine (SVM) classifiers by adding three important features: (i) we introduce a regularization constraint to induce a sparse classifier; (ii) we devise a method that partitions the positive class into clusters and selects a sparse SVM classifier for each cluster; and (iii) we develop a method to optimize the values of controllable variables in order to reduce the number of data points which are predicted to have an undesirable outcome, which, in our setting, coincides with being in the positive class. The latter feature leads to personalized prescriptions/recommendations. We apply our methods to the problem of predicting and preventing hospital readmissions within 30-days from discharge for patients that underwent a general surgical procedure. To that end, we leverage a large dataset containing over 2.28 million patients who had surgeries in the period 2011--2014 in the U.S. The dataset has been collected as part of the American College of Surgeons National Surgical Quality Improvement Program (NSQIP).

stat.AP↗