arXiv subjects

Ahmadreza Moradipari

Publications and source records attributed to Ahmadreza Moradipari.

28 records · Page 2Linked to original sources

arXiv2022

Feature and Parameter Selection in Stochastic Linear Bandits

We study two model selection settings in stochastic linear bandits (LB). In the first setting, which we refer to as feature selection, the expected reward of the LB problem is in the linear span of at least one of $M$ feature maps (models). In the second setting, the reward parameter of the LB problem is arbitrarily selected from $M$ models represented as (possibly) overlapping balls in $\mathbb R^d$. However, the agent only has access to misspecified models, i.e.,~estimates of the centers and radii of the balls. We refer to this setting as parameter selection. For each setting, we develop and analyze a computationally efficient algorithm that is based on a reduction from bandits to full-information problems. This allows us to obtain regret bounds that are not worse (up to a $\sqrt{\log M}$ factor) than the case where the true model is known. This is the best-reported dependence on the number of models $M$ in these settings. Finally, we empirically show the effectiveness of our algorithms using synthetic and real-world experiments.

cs.LG↗

arXiv2022

Multi-Environment Meta-Learning in Stochastic Linear Bandits

In this work we investigate meta-learning (or learning-to-learn) approaches in multi-task linear stochastic bandit problems that can originate from multiple environments. Inspired by the work of [1] on meta-learning in a sequence of linear bandit problems whose parameters are sampled from a single distribution (i.e., a single environment), here we consider the feasibility of meta-learning when task parameters are drawn from a mixture distribution instead. For this problem, we propose a regularized version of the OFUL algorithm that, when trained on tasks with labeled environments, achieves low regret on a new task without requiring knowledge of the environment from which the new task originates. Specifically, our regret bound for the new algorithm captures the effect of environment misclassification and highlights the benefits over learning each task separately or meta-learning without recognition of the distinct mixture components.

cs.LG↗

arXiv2022

Collaborative Multi-agent Stochastic Linear Bandits

We study a collaborative multi-agent stochastic linear bandit setting, where $N$ agents that form a network communicate locally to minimize their overall regret. In this setting, each agent has its own linear bandit problem (its own reward parameter) and the goal is to select the best global action w.r.t. the average of their reward parameters. At each round, each agent proposes an action, and one action is randomly selected and played as the network action. All the agents observe the corresponding rewards of the played actions and use an accelerated consensus procedure to compute an estimate of the average of the rewards obtained by all the agents. We propose a distributed upper confidence bound (UCB) algorithm and prove a high probability bound on its $T$-round regret in which we include a linear growth of regret associated with each communication round. Our regret bound is of order $\mathcal{O}\Big(\sqrt{\frac{T}{N \log(1/|λ_2|)}}\cdot (\log T)^2\Big)$, where $λ_2$ is the second largest (in absolute value) eigenvalue of the communication matrix.

cs.LG↗

arXiv2020

Stage-wise Conservative Linear Bandits

We study stage-wise conservative linear stochastic bandits: an instance of bandit optimization, which accounts for (unknown) safety constraints that appear in applications such as online advertising and medical trials. At each stage, the learner must choose actions that not only maximize cumulative reward across the entire time horizon but further satisfy a linear baseline constraint that takes the form of a lower bound on the instantaneous reward. For this problem, we present two novel algorithms, stage-wise conservative linear Thompson Sampling (SCLTS) and stage-wise conservative linear UCB (SCLUCB), that respect the baseline constraints and enjoy probabilistic regret bounds of order O(\sqrt{T} \log^{3/2}T) and O(\sqrt{T} \log T), respectively. Notably, the proposed algorithms can be adjusted with only minor modifications to tackle different problem variations, such as constraints with bandit-feedback, or an unknown sequence of baseline actions. We discuss these and other improvements over the state-of-the-art. For instance, compared to existing solutions, we show that SCLTS plays the (non-optimal) baseline action at most O(\log{T}) times (compared to O(\sqrt{T})). Finally, we make connections to another studied form of safety constraints that takes the form of an upper bound on the instantaneous reward. While this incurs additional complexity to the learning process as the optimal action is not guaranteed to belong to the safe set at each round, we show that SCLUCB can properly adjust in this setting via a simple modification.

cs.LG↗

arXiv2020

Mobility-Aware Electric Vehicle Fast Charging Load Models with Geographical Price Variations

We study the traffic patterns as well as the charging patterns of a population of cost-minimizing EV owners traveling and charging within a transportation network equipped with fast charging stations (FCSs). Specifically, we study how the charging network operator (CNO) can influence where EV users charge in order to optimize the utilization of fast charging stations. These charging decisions of private EV owners affect aggregate congestion at stations (i.e., waiting time) as well as the aggregate EV charging load across the network. In this work, we capture the resulting equilibrium wait times and electricity load through a so-called \textit{traffic and charge assignment problem} (TCAP) in a fast charging station network. Our formulation allows us to: 1) Study the expected station wait times as well as the probability distribution of aggregate charging load of EVs in a FCS network in a mobility-aware fashion (an aspect unique to our work), while accounting for heterogeneities in users' travel patterns, energy demands, and geographically variant electricity prices. 2) Analytically characterize the special threshold-based structure that determines how EV owners choose where to charge their vehicle at equilibrium, in response to the FCS's charging price structure, users' energy demands, and users' mobility patterns. 3) Provide a convex optimization problem formulation to identify the network's unique equilibrium. Furthermore, we illustrate how to induce a socially optimal charging behavior by deriving the socially optimal plug-in fees and electricity prices at the charging stations.

eess.SY↗

arXiv2020

Constrained Thompson Sampling for Real-Time Electricity Pricing with Grid Reliability Constraints

We consider the problem of an aggregator attempting to learn customers' load flexibility models while implementing a load shaping program by means of broadcasting daily dispatch signals. We adopt a multi-armed bandit formulation to account for the stochastic and unknown nature of customers' responses to dispatch signals. We propose a constrained Thompson sampling heuristic, Con-TS-RTP, that accounts for various possible aggregator objectives (e.g., to reduce demand at peak hours, integrate more intermittent renewable generation, track a desired daily load profile, etc) and takes into account the operational constraints of a distribution system to avoid potential grid failures as a result of uncertainty in the customers' response. We provide a discussion on the regret bounds for our algorithm as well as a discussion on the operational reliability of the distribution system's constraints being upheld throughout the learning process.

eess.SY↗

arXiv2020

Safe Linear Thompson Sampling with Side Information

The design and performance analysis of bandit algorithms in the presence of stage-wise safety or reliability constraints has recently garnered significant interest. In this work, we consider the linear stochastic bandit problem under additional \textit{linear safety constraints} that need to be satisfied at each round. We provide a new safe algorithm based on linear Thompson Sampling (TS) for this problem and show a frequentist regret of order $\mathcal{O} (d^{3/2}\log^{1/2}d \cdot T^{1/2}\log^{3/2}T)$, which remarkably matches the results provided by (Abeille et al., 2017) for the standard linear TS algorithm in the absence of safety constraints. We compare the performance of our algorithm with UCB-based safe algorithms and highlight how the inherently randomized nature of TS leads to a superior performance in expanding the set of safe actions the algorithm has access to at each round.

cs.LG↗

arXiv2019

Mobility-Aware Smart Charging of Electric Bus Fleets

We study the joint route assignment and charge scheduling problem of a transit system dispatcher operating a fleet of electric buses in order to maximize solar energy integration and reduce energy costs. Specifically, we consider a complex bus transit system with preexisting routes, limited charging infrastructure, limited number of electric buses, and time-varying electricity rates. We present a mixed integer linear program (MILP) that yields the minimal cost daily operation strategy for the fleet (i.e., route assignments and charging schedules using daily solar forecasts). We present numerical results from a real-world case study with Stanford University's Marguerite Shuttle (a large-scale electric bus fleet) to demonstrate the validity of our solution and highlight the significant cost savings compared to the status quo.

eess.SY↗

arXiv2019

Pricing and Routing Mechanisms for Differentiated Services in an Electric Vehicle Public Charging Station Network

We consider a Charging Network Operator (CNO) that owns a network of Electric Vehicle (EV) public charging stations and wishes to offer a menu of differentiated service options for access to its stations. This involves designing optimal pricing and routing schemes for the setting where users cannot directly choose which station they use. Instead, they choose their priority level and energy request amount from the differentiated service menu, and then the CNO directly assigns them to a station on their path. This allows higher priority users to experience lower wait times at stations, and allows the CNO to directly manage demand, exerting a higher level of control that can be used to manage the effect of EV on the grid and control station wait times. We consider the scenarios where the CNO is a social welfare-maximizing or a profit-maximizing entity, and in both cases, design pricing-routing policies that ensure users reveal their true parameters to the CNO.

eess.SY↗

arXiv2017

Using Empirical Covariance Matrix in Enhancing Prediction Accuracy of Linear Models with Missing Information

Inference and Estimation in Missing Information (MI) scenarios are important topics in Statistical Learning Theory and Machine Learning (ML). In ML literature, attempts have been made to enhance prediction through precise feature selection methods. In sparse linear models, LASSO is well-known in extracting the desired support of the signal and resisting against noisy systems. When sparse models are also suffering from MI, the sparse recovery and inference of the missing models are taken into account simultaneously. In this paper, we will introduce an approach which enjoys sparse regression and covariance matrix estimation to improve matrix completion accuracy, and as a result enhancing feature selection preciseness which leads to reduction in prediction Mean Squared Error (MSE). We will compare the effect of employing covariance matrix in enhancing estimation accuracy to the case it is not used in feature selection. Simulations show the improvement in the performance as compared to the case where the covariance matrix estimation is not used.

stat.ML↗