arXiv subjects

Eilyan Bitar

Publications and source records attributed to Eilyan Bitar.

At least 19 recordsLinked to original sources

arXiv2026

Wasserstein Distributionally Robust Risk-Sensitive Estimation via Conditional Value-at-Risk

We propose a distributionally robust approach to risk-sensitive estimation of an unknown signal x from an observed signal y. The observation and unknown signal are modeled as random vectors whose joint probability distribution is unknown, but assumed to belong to a given type-2 Wasserstein ball of distributions, termed the ambiguity set. The performance of an estimator is measured according to the conditional value-at-risk (CVaR) of the squared estimation error. Within this framework, we study the problem of computing affine estimators that minimize the worst-case CVaR over all distributions in the given ambiguity set. As our main result, we show that, when the nominal distribution at the center of the Wasserstein ball is finitely supported, such estimators can be exactly computed by solving a tractable semidefinite program. We evaluate the proposed estimators on a wholesale electricity price forecasting task using real market data and show that they deliver lower out-of-sample CVaR of squared error compared to existing methods.

cs.LG↗

arXiv2025

Distributionally Robust Regret Optimal Control Under Moment-Based Ambiguity Sets

We consider a class of finite-horizon, linear-quadratic stochastic control problems, where the probability distribution governing the noise process is unknown but assumed to belong to an ambiguity set consisting of all distributions whose mean and covariance lie within norm balls centered at given nominal values. To cope with this ambiguity, we design causal affine control policies to minimize the worst-case expected regret over all distributions in the ambiguity set. The resulting minimax optimal control problem is shown to admit an equivalent reformulation as a tractable convex program, which can be interpreted as a regularized version of the nominal linear-quadratic stochastic control problem. Based on the dual of this convex reformulation, we develop a scalable projected subgradient method for computing optimal controllers to arbitrary accuracy. Numerical experiments are provided to compare the proposed method with state-of-the-art data-driven control design methods.

math.OC↗

arXiv2024

Distributionally Robust Regret Minimization

We consider decision-making problems involving the optimization of linear objective functions with uncertain coefficients. The probability distribution of the coefficients--which are assumed to be stochastic in nature--is unknown to the decision maker but is assumed to lie within a given ambiguity set, defined as a type-1 Wasserstein ball centered at a given nominal distribution. To account for this uncertainty, we minimize the worst-case expected regret over all distributions in the ambiguity set. Here, the (ex post) regret experienced by the decision maker is defined as the difference between the cost incurred by a chosen decision given a particular realization of the objective coefficients and the minimum achievable cost with perfect knowledge of the coefficients at the outset. For this class of ambiguity sets, the worst-case expected regret is shown to equal the expected regret under the nominal distribution plus a regularization term that has the effect of drawing optimal solutions toward the "center" of the feasible region as the radius of the ambiguity set increases. This novel form of regularization is also shown to arise when minimizing the worst-case conditional value-at-risk (CVaR) of regret. We show that, under certain conditions, distributionally robust regret minimization problems over type-1 Wasserstein balls can be recast as tractable finite-dimensional convex programs.

math.OC↗

arXiv2024

When are Lossy Energy Storage Optimization Models Convex?

We examine a class of optimization problems involving the optimal operation of a single lossy energy storage system, where energy losses occur during charging and discharging. These inefficiencies typically lead to a nonconvex set of feasible charging and discharging power profiles. In this paper, we derive an equivalent reformulation of this class of optimization problems by eliminating the charging and discharging power variables and recasting the problem entirely in terms of the storage state-of-charge variables. We show that the feasible set of the proposed reformulation is always convex. We also provide sufficient conditions under which the objective function of the proposed reformulation is guaranteed to be convex. The conditions provided both unify and generalize many existing conditions for convexity in the literature.

eess.SY↗

arXiv2024

An Efficient Method for Quantifying the Aggregate Flexibility of Plug-in Electric Vehicle Populations

Plug-in electric vehicles (EVs) are widely recognized as being highly flexible electric loads that can be pooled and controlled via aggregators to provide low-cost energy and ancillary services to wholesale electricity markets. To participate in these markets, an aggregator must encode the aggregate flexibility of the population of EVs under their command as a single polytope that is compliant with existing market rules. To this end, we investigate the problem of characterizing the aggregate flexibility set of a heterogeneous population of EVs whose individual flexibility sets are given as convex polytopes in half-space representation. As the exact computation of the aggregate flexibility set -- the Minkowski sum of the individual flexibility sets -- is known to be intractable, we study the problem of computing maximum-volume inner approximations to the aggregate flexibility set by optimizing over affine transformations of a given convex polytope in half-space representation. We show how to conservatively approximate these set containment problems as linear programs that scale polynomially with the number and dimension of the individual flexibility sets. The inner approximation methods provided in this paper generalize and improve upon existing methods from the literature. We illustrate the improvement in approximation accuracy and performance achievable by our methods with numerical experiments.

eess.SY↗

arXiv2023

A Distributionally Robust Approach to Regret Optimal Control using the Wasserstein Distance

This paper proposes a distributionally robust approach to regret optimal control of discrete-time linear dynamical systems with quadratic costs subject to a stochastic additive disturbance on the state process. The underlying probability distribution of the disturbance process is unknown, but assumed to lie in a given ball of distributions defined in terms of the type-2 Wasserstein distance. In this framework, strictly causal linear disturbance feedback controllers are designed to minimize the worst-case expected regret. The regret incurred by a controller is defined as the difference between the cost it incurs in response to a realization of the disturbance process and the cost incurred by the optimal noncausal controller which has perfect knowledge of the disturbance process realization at the outset. Building on a well-established duality theory for optimal transport problems, we derive a reformulation of the minimax regret optimal control problem as a tractable semidefinite program. Using the equivalent dual reformulation, we characterize a worst-case distribution achieving the worst-case expected regret in relation to the distribution at the center of the Wasserstein ball. We compare the minimax regret optimal control design method with the distributionally robust optimal control approach using an illustrative example and numerical experiments.

math.OC↗

arXiv2023

A Multi-Battery Model for the Aggregate Flexibility of Heterogeneous Electric Vehicles

The increasing prevalence of electric vehicles (EVs) in the transportation sector will introduce a large number of highly flexible electric loads that EV aggregators can pool and control to provide energy and ancillary services to the wholesale electricity market. To integrate large populations of EVs into electricity market operations, aggregators must express the aggregate flexibility of the EVs under their control in the form of a small number of energy storage (battery) resources that accurately capture the supply/demand capabilities of the individual EVs as a collective. To this end, we propose a novel multi-battery flexibility model defined as a linear combination of a small number of base sets (termed batteries) that reflect the differing geometric shapes of the individual EV flexibility sets, and suggest a clustering approach to identify these base sets. We study the problem of computing a multi-battery flexibility set that has minimum Hausdorff distance to the aggregate flexibility set, subject to the constraint that the multi-battery flexibility set be a subset of the aggregate flexibility set. We show how to conservatively approximate this problem with a tractable convex program, and illustrate the performance achievable by our method with several numerical experiments.

eess.SY↗

arXiv2023

Achieving Reliable Coordination of Residential Plug-in Electric Vehicle Charging: A Pilot Study

Wide-scale electrification of the transportation sector will require careful planning and coordination with the power grid. Left unmanaged, uncoordinated charging of electric vehicles (EVs) at increased levels of penetration will amplify existing peak loads, potentially outstripping the grid's capacity to reliably meet demand. In this paper, we report findings from the OptimizEV Project - a real-world pilot study in Upstate New York exploring a novel approach to coordinated residential EV charging. The proposed coordination mechanism seeks to harness the latent flexibility in EV charging by offering EV owners monetary incentives to delay the time required to charge their EVs. Each time an EV owner initiates a charging session, they specify how long they intend to leave their vehicle plugged in by selecting from a menu of deadlines that offers lower electricity prices the longer they're willing to delay the time required to charge their EV. Given a collection of active charging requests, a smart charging system dynamically optimizes the power being drawn by each EV in real time to minimize strain on the grid, while ensuring that each customer's car is fully charged by its deadline. Under the proposed incentive mechanism, we find that customers are frequently willing to engage in optimized charging sessions, allowing the system to delay the completion of their charging requests by more than eight hours on average. Using the flexibility provided by customers, the smart charging system was shown to be highly effective in shifting the majority of EV charging loads off-peak to fill the night-time valley of the aggregate load curve. Customer opt-in rates remained stable over the span of the study, providing empirical evidence in support of the proposed coordination mechanism as a potentially viable "non-wires alternative" to meet the increased demand for electricity driven growing EV adoption.

eess.SY↗

arXiv2022

Data-Driven Approximations of Chance Constrained Programs in Nonstationary Environments

We study sample average approximations (SAA) of chance constrained programs. SAA methods typically approximate the actual distribution in the chance constraint using an empirical distribution constructed from random samples assumed to be independent and identically distributed according to the actual distribution. In this paper, we consider a nonstationary variant of this problem, where the random samples are assumed to be independently drawn in a sequential fashion from an unknown and possibly time-varying distribution. This nonstationarity may be driven by changing environmental conditions present in many real-world applications. To account for the potential nonstationarity in the data generation process, we propose a novel robust SAA method exploiting information about the Wasserstein distance between the sequence of data-generating distributions and the actual chance constraint distribution. As a key result, we obtain distribution-free estimates of the sample size required to ensure that the robust SAA method will yield solutions that are feasible for the chance constraint under the actual distribution with high confidence.

math.OC↗

arXiv2022

Exploring Adversarial Robustness of Multi-Sensor Perception Systems in Self Driving

Modern self-driving perception systems have been shown to improve upon processing complementary inputs such as LiDAR with images. In isolation, 2D images have been found to be extremely vulnerable to adversarial attacks. Yet, there have been limited studies on the adversarial robustness of multi-modal models that fuse LiDAR features with image features. Furthermore, existing works do not consider physically realizable perturbations that are consistent across the input modalities. In this paper, we showcase practical susceptibilities of multi-sensor detection by placing an adversarial object on top of a host vehicle. We focus on physically realizable and input-agnostic attacks as they are feasible to execute in practice, and show that a single universal adversary can hide different host vehicles from state-of-the-art multi-modal detectors. Our experiments demonstrate that successful attacks are primarily caused by easily corrupted image features. Furthermore, we find that in modern sensor fusion methods which project image features into 3D, adversarial attacks can exploit the projection process to generate false positives across distant regions in 3D. Towards more robust multi-modal perception systems, we show that adversarial training with feature denoising can boost robustness to such attacks significantly. However, we find that standard adversarial defenses still struggle to prevent false positives which are also caused by inaccurate associations between 3D LiDAR points and 2D pixels.

cs.CV↗

arXiv2021

Design of Robust Decentralized Controllers via Assume-Guarantee Contracts

We consider the decentralized control of a discrete-time time-varying linear system subject to additive disturbances and polyhedral constraints on the state and input trajectories. The underlying system is composed of a finite collection of dynamically coupled subsystems, where each subsystem is assumed to have a dedicated local controller. The decentralization of information is expressed according to sparsity constraints on the state measurements that each local controller has access to. We investigate the design of decentralized controllers that are affinely parameterized in their measurement history. For problems with partially nested information structures, the optimization over such restricted policy spaces is known to be convex. Convexity is not, however, guaranteed under more general (nonclassical) information structures, where the information available to one local controller can be affected by control actions that it cannot reconstruct. To address the nonconvexity that arises in such problems, we propose an approach to decentralized control design where such information-coupling states are effectively treated as disturbances whose trajectories are constrained to take values in ellipsoidal "contract" sets whose location, scale, and orientation are jointly optimized with the underlying affine decentralized control policy. We establish a structural condition on the space of allowable contracts that facilitates the joint optimization over the control policy and the contract set via semidefinite programming.

math.OC↗

arXiv2020

Transparency and Control in Platforms for Networked Markets

In this paper, we analyze the worst case efficiency loss of online platform designs under a networked Cournot competition model. Inspired by some of the largest platforms in operation today, the platform designs that we consider examine the trade-off between transparency and control. Our results show that open access designs incentivize increased production towards perfectly competitive levels and limit efficiency loss, while controlled allocation designs lead to producer-platform incentive misalignment, resulting in low participation and unbounded efficiency loss. We also show that discriminatory access designs balance transparency and control, achieving the best of both worlds by maintaining high participation rates while limiting efficiency loss.

cs.GT↗

arXiv2020

Nonparametric Estimation of Uncertainty Sets for Robust Optimization

We investigate a data-driven approach to constructing uncertainty sets for robust optimization problems, where the uncertain problem parameters are modeled as random variables whose joint probability distribution is not known. Relying only on independent samples drawn from this distribution, we provide a nonparametric method to estimate uncertainty sets whose probability mass is guaranteed to approximate a given target mass within a given tolerance with high confidence. The nonparametric estimators that we consider are also shown to obey distribution-free finite-sample performance bounds that imply their convergence in probability to the given target mass. In addition to being efficient to compute, the proposed estimators result in uncertainty sets that yield computationally tractable robust optimization problems for a large family of constraint functions.

math.OC↗

arXiv2020

Decentralized Control of Constrained Linear Systems via Assume-Guarantee Contracts

We consider the decentralized control of a discrete-time, linear system subject to exogenous disturbances and polyhedral constraints on the state and input trajectories. The underlying system is composed of a finite collection of dynamically coupled subsystems, where each subsystem is assumed to have a dedicated local controller. The decentralization of information is expressed according to sparsity constraints on the state measurements that each local controller has access to. In this context, we investigate the design of decentralized controllers that are affinely parameterized in their measurement history. For problems with partially nested information structures, the optimization over such policy spaces is known to be convex. Convexity is not, however, guaranteed under more general (nonclassical) information structures in which the information available to one local controller can be affected by control actions that it cannot access or reconstruct. With the aim of alleviating the nonconvexity that arises in such problems, we propose an approach to decentralized control design where the information-coupling states are effectively treated as disturbances whose trajectories are constrained to take values in ellipsoidal contract sets whose location, scale, and orientation are jointly optimized with the underlying affine decentralized control policy. We establish a natural structural condition on the space of allowable contracts that facilitates the joint optimization over the control policy and the contract set via semidefinite programming.

math.OC↗

arXiv2019

Safe Linear Stochastic Bandits

We introduce the safe linear stochastic bandit framework---a generalization of linear stochastic bandits---where, in each stage, the learner is required to select an arm with an expected reward that is no less than a predetermined (safe) threshold with high probability. We assume that the learner initially has knowledge of an arm that is known to be safe, but not necessarily optimal. Leveraging on this assumption, we introduce a learning algorithm that systematically combines known safe arms with exploratory arms to safely expand the set of safe arms over time, while facilitating safe greedy exploitation in subsequent stages. In addition to ensuring the satisfaction of the safety constraint at every stage of play, the proposed algorithm is shown to exhibit an expected regret that is no more than $O(\sqrt{T}\log (T))$ after $T$ stages of play.

stat.ML↗

arXiv2019

A Convex Information Relaxation for Constrained Decentralized Control Design Problems

We describe a convex programming approach to the calculation of lower bounds on the minimum cost of constrained decentralized control problems with nonclassical information structures. The class of problems we consider entail the decentralized output feedback control of a linear time-varying system over a finite horizon, subject to polyhedral constraints on the state and input trajectories, and sparsity constraints on the controller's information structure. As the determination of optimal control policies for such systems is known to be computationally intractable in general, considerable effort has been made in the literature to identify efficiently computable, albeit suboptimal, feasible control policies. The construction of computationally tractable bounds on their suboptimality is the primary motivation for the techniques developed in this note. Specifically, given a decentralized control problem with nonclassical information, we characterize an expansion of the given information structure, which ensures its partial nestedness, while maximizing the optimal value of the resulting decentralized control problem under the expanded information structure. The resulting decentralized control problem is cast as an infinite-dimensional convex program, which is further relaxed via a partial dualization and restriction to affine dual control policies. The resulting problem is a finite-dimensional conic program whose optimal value is a provable lower bound on the minimum cost of the original constrained decentralized control problem.

math.OC↗

arXiv2019

A Structural Characterization of Market Power in Electric Power Networks

We consider a market in which capacity-constrained generators compete in scalar-parameterized supply functions to serve an inelastic demand spread throughout a transmission constrained power network. The market clears according to a locational marginal pricing mechanism, in which the independent system operator (ISO) determines the generators' production quantities to minimize the revealed cost of meeting demand, while ensuring that network transmission and generator capacity constraints are met. Under the stylizing assumption that both the ISO and generators choose their strategies simultaneously, we establish the existence of Nash equilibria for the underlying market, and derive an upper bound on the allocative efficiency loss at Nash equilibrium relative to the socially optimal level. We also characterize an upper bound on the markup of locational marginal prices at Nash equilibrium above their perfectly competitive levels. Of particular relevance to ex ante market power monitoring, these bounds reveal the role of certain market structures---specifically, the \emph{market share} and \emph{residual supply index} of a producer---in predicting the degree to which that producer is able to exercise market power to influence the market outcome to its advantage. Finally, restricting our attention to the simpler setting of a two-node power network, we provide a characterization of market structures under which a Braess-like paradox occurs due to the exercise of market power---that is to say, we provide a necessary and sufficient condition on market structure under which the strengthening of the network's transmission line capacity results in the (counterintuitive) increase in the total cost of generation at Nash equilibrium.

cs.GT↗

arXiv2018

On the Marginal Value of Electricity Storage

We investigate the problem of characterizing the economic value of energy storage capacity to a wind power producer (WPP) that sells its energy in a conventional two-settlement electricity market. The WPP can offer a forward contract to supply power in the day-ahead market, subject to financial penalties for imbalances between the contracted power and the power that is delivered in real-time. We consider the setting in which the WPP has access to a co-located energy storage system, and can thus reshape its wind power production subject to its storage capacity constraints. Modeling wind power as a random process, we show that the problem of determining optimal forward contract offerings--given recourse with storage--is convex. We further establish that the maximum expected profit is concave and non-decreasing in the energy storage capacity, which reveals that the greatest marginal benefit from energy storage is derived from initial investment in small storage capacity. We provide a characterization of the marginal value of small energy storage capacity to the WPP. The formulae we derive shed light on the relationship between the value of storage and certain statistical measures of variability in the underlying wind power process.

math.OC↗