arXiv subjects

Ashish Cherukuri

Publications and source records attributed to Ashish Cherukuri.

At least 19 recordsLinked to original sources

arXiv2026

Distributionally Robust Federated Learning with Multi-Source Data

Federated learning trains a shared model from private client data. In practice, data-generating distributions may differ, and the true mixture across clients is often unknown, making the underlying group distribution difficult to specify. Existing approaches address cross-client mixture uncertainty by optimizing against the worst-case mixture, yet assume accurate client-wise distribution estimates. However, these estimates can be unreliable when based on finite samples. To handle both cross-client mixture uncertainty and within-client distributional ambiguity, we construct a global ambiguity set as the union of admissible mixtures of local ambiguity sets. The construction allows client-specific ambiguity radii and admits a client-wise separable reformulation. Leveraging this structure, we establish a high-probability out-of-sample performance guarantee. We further develop a federated algorithm for a penalty-based reformulation and prove its convergence under milder regularity conditions. Simulations validate the algorithm's effectiveness.

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arXiv2026

Stability of Information-Based Routing in Dynamic Transportation Networks

Recent studies on transportation networks have shown that real-time route guidance can inadvertently induce congestion or oscillatory traffic patterns. Nevertheless, such technologies also offer a promising opportunity to manage traffic non-intrusively by shaping the information delivered to users, thereby mitigating congestion and enhancing network stability. A key step toward this goal is to identify information signals that ensure the existence of an equilibrium with desirable stability and convergence properties. This challenge is particularly relevant when traffic density and routing dynamics evolve concurrently, as increasingly occurs with digital signaling and real-time navigation technologies. To address this, we analyze a parallel-path transportation network with a single origin-destination pair, incorporating joint traffic density and logit-based routing dynamics that evolve at the same timescale. We characterize a class of density-dependent traffic information that guarantees a unique equilibrium in the free-flow regime, ensures its asymptotic stability, and keeps traffic densities within the free-flow region for all time. The theoretical results are complemented by a numerical case study demonstrating how the framework can inform the design of traffic information that reduces total travel time without compromising credibility.

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arXiv2025

Distributed alternating gradient descent for convex semi-infinite programs over a network

This paper presents a first-order distributed algorithm for solving a convex semi-infinite program (SIP) over a time-varying network. In this setting, the objective function associated with the optimization problem is a summation of a set of functions, each held by one node in a network. The semi-infinite constraint, on the other hand, is known to all agents. The nodes collectively aim to solve the problem using local data about the objective and limited communication capabilities depending on the network topology. Our algorithm is built on three key ingredients: consensus step, gradient descent in the local objective, and local gradient descent iterations in the constraint at a node when the estimate violates the semi-infinite constraint. The algorithm is constructed, and its parameters are prescribed in such a way that the iterates held by each agent provably converge to an optimizer. That is, as the algorithm progresses, the estimates achieve consensus, and the constraint violation and the error in the optimal value are bounded above by vanishing terms. Simulation examples illustrate our results.

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arXiv2023

Wasserstein distributionally robust risk-constrained iterative MPC for motion planning: computationally efficient approximations

This paper considers a risk-constrained motion planning problem and aims to find the solution combining the concepts of iterative model predictive control (MPC) and data-driven distributionally robust (DR) risk-constrained optimization. In the iterative MPC, at each iteration, safe states visited and stored in the previous iterations are imposed as terminal constraints. Furthermore, samples collected during the iteration are used in the subsequent iterations to tune the ambiguity set of the DR constraints employed in the MPC. In this method, the MPC problem becomes computationally burdensome when the iteration number goes high. To overcome this challenge, the emphasis of this paper is to reduce the real-time computational effort using two approximations. First one involves clustering of data at the beginning of each iteration and modifying the ambiguity set for the MPC scheme so that safety guarantees still holds. The second approximation considers determining DR-safe regions at the start of iteration and constraining the state in the MPC scheme to such safe sets. We analyze the computational tractability of these approximations and present a simulation example that considers path planning in the presence of randomly moving obstacle.

math.OC↗

arXiv2023

Wardrop equilibrium and Braess's paradox for varying demand

This work explores the relationship between the set of Wardrop equilibria~(WE) of a routing game, the total demand of that game, and the occurrence of Braess's paradox~(BP). The BP formalizes the counter-intuitive fact that for some networks, removing a path from the network decreases congestion at WE. For a single origin-destination routing games with affine cost functions, the first part of this work provides tools for analyzing the evolution of the WE as the demand varies. It characterizes the piece-wise affine nature of this dependence by showing that the set of directions in which the WE can vary in each piece is the solution of a variational inequality problem. In the process we establish various properties of changes in the set of used and minimal-cost paths as demand varies. As a consequence of these characterizations, we derive a procedure to obtain the WE for all demands above a certain threshold. The second part of the paper deals with detecting the presence of BP in a network. We supply a number of sufficient conditions that reveal the presence of BP and that are computationally tractable. We also discuss a different perspective on BP, where we establish that a path causing BP at a particular demand must be strictly beneficial to the network at a lower demand. Several examples throughout this work illustrate and elaborate our findings.

cs.GT↗

arXiv2023

Iterative risk-constrained model predictive control: A data-driven distributionally robust approach

This paper proposes an iterative distributionally robust model predictive control (MPC) scheme to solve a risk-constrained infinite-horizon optimal control problem. In each iteration, the algorithm generates a trajectory from the starting point to the target equilibrium state with the aim of respecting risk constraints with high probability (that encodes safe operation of the system) and improving the cost of the trajectory as compared to previous iterations. At the end of each iteration, the visited states and observed samples of the uncertainty are stored and accumulated with the previous observations. For each iteration, the states stored previously are considered as terminal constraints of the MPC scheme, and samples obtained thus far are used to construct distributionally robust risk constraints. As iterations progress, more data is obtained and the environment is explored progressively to ensure better safety and cost optimality. We prove that the MPC scheme in each iteration is recursively feasible and the resulting trajectories converge asymptotically to the target while ensuring safety with high probability. We identify conditions under which the cost-to-go reduces as iterations progress. For systems with locally one-step reachable target, we specify scenarios that ensure finite-time convergence of iterations. We provide computationally tractable reformulations of the risk constraints for total variation and Wasserstein distance-based ambiguity sets. A simulation example illustrates the application of our results in finding a risk-constrained path for two mobile robots facing an uncertain obstacle.

math.OC↗

arXiv2023

Inferring the prior in routing games using public signalling

This paper considers Bayesian persuasion for routing games where information about the uncertain state of the network is provided by a traffic information system (TIS) using public signals. In this setup, the TIS commits to a signalling scheme and participants form a posterior belief about the state of the network based on prior beliefs and the received signal. They subsequently select routes minimizing their individual expected travel time under their posterior beliefs, giving rise to a Wardrop equilibrium. We investigate how the TIS can infer the prior beliefs held by the participants by designing suitable signalling schemes, and observing the equilibrium flows under different signals. We show that under mild conditions a signalling scheme that allows for exact inference of the prior exists. We then provide an iterative algorithm that finds such a scheme in a finite number of steps. We show that schemes designed by our algorithm are robust, in the sense that they can still identify the prior after a small enough perturbation. We also investigate the case where the population is divided among multiple priors, and give conditions under which the fraction associated to each prior can be identified. Several examples illustrate our results.

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arXiv2022

Stochastic approximation approaches for CVaR-based variational inequalities

This paper considers variational inequalities (VI) defined by the conditional value-at-risk (CVaR) of uncertain functions and provides three stochastic approximation schemes to solve them. All methods use an empirical estimate of the CVaR at each iteration. The first algorithm constrains the iterates to the feasible set using projection. To overcome the computational burden of projections, the second one handles inequality and equality constraints defining the feasible set differently. Particularly, projection onto to the affine subspace defined by the equality constraints is achieved by matrix multiplication and inequalities are handled by using penalty functions. Finally, the third algorithm discards projections altogether by introducing multiplier updates. We establish asymptotic convergence of all our schemes to any arbitrary neighborhood of the solution of the VI. A simulation example concerning a network routing game illustrates our theoretical findings.

math.OC↗

arXiv2022

Cross apprenticeship learning framework: Properties and solution approaches

Apprenticeship learning is a framework in which an agent learns a policy to perform a given task in an environment using example trajectories provided by an expert. In the real world, one might have access to expert trajectories in different environments where the system dynamics is different while the learning task is the same. For such scenarios, two types of learning objectives can be defined. One where the learned policy performs very well in one specific environment and another when it performs well across all environments. To balance these two objectives in a principled way, our work presents the cross apprenticeship learning (CAL) framework. This consists of an optimization problem where an optimal policy for each environment is sought while ensuring that all policies remain close to each other. This nearness is facilitated by one tuning parameter in the optimization problem. We derive properties of the optimizers of the problem as the tuning parameter varies. Since the problem is nonconvex, we provide a convex outer approximation. Finally, we demonstrate the attributes of our framework in the context of a navigation task in a windy gridworld environment.

math.OC↗

arXiv2022

Sample Average Approximation of Conditional Value-at-risk based Variational Inequalities

This paper focuses on a class of variational inequalities (VIs), where the map defining the VI is given by the component-wise conditional value-at-risk (CVaR) of a random function. We focus on solving the VI using sample average approximation, where solutions of the VI are estimated with solutions of a sample average VI that uses empirical estimates of the CVaRs. We establish two properties for this scheme. First, under continuity of the random map and the uncertainty taking values in a bounded set, we prove asymptotic consistency, establishing almost sure convergence of the solution of the sample average problem to the true solution. Second, under the additional assumption of random functions being Lipschitz, we prove exponential convergence where the probability of the distance between an approximate solution and the true solution being smaller than any constant approaches unity exponentially fast. The exponential decay bound is refined for the case where random functions have a specific separable form in the decision variable and uncertainty. We adapt these results to the case of uncertain routing games and derive explicit sample guarantees for obtaining a CVaR-based Wardrop equilibria using the sample average procedure. We illustrate our theoretical findings by approximating the CVaR-based Wardrop equilibria for a modified Sioux Falls network.

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arXiv2022

Data-driven distributionally robust optimization over a network via distributed semi-infinite programming

This paper focuses on solving a data-driven distributionally robust optimization problem over a network of agents. The agents aim to minimize the worst-case expected cost computed over a Wasserstein ambiguity set that is centered at the empirical distribution. The samples of the uncertainty are distributed across the agents. Our approach consists of reformulating the problem as a semi-infinite program and then designing a distributed algorithm that solves a generic semi-infinite problem that has the same information structure as the reformulated problem. In particular, the decision variables consist of both local ones that agents are free to optimize over and global ones where they need to agree on. Our distributed algorithm is an iterative procedure that combines the notions of distributed ADMM and the cutting-surface method. We show that the iterates converge asymptotically to a solution of the distributionally robust problem to any pre-specified accuracy. Simulations illustrate our results.

math.OC↗

arXiv2022

A two-step approach to Wasserstein distributionally robust chance- and security-constrained dispatch

This paper considers a security constrained dispatch problem involving generation and line contingencies in the presence of the renewable generation. The uncertainty due to renewables is modeled using joint chance-constraint and the mismatch caused by contingencies and renewables are handled using reserves. We consider a distributionally robust approach to solve the chance-constrained program. We assume that samples of the uncertainty are available. Using them, we construct a set of distributions, termed ambiguity set, containing all distributions that are close to the empirical distribution under the Wasserstein metric. The chance constraint is imposed for all distributions in the ambiguity set to form the distributionally robust optimization problem. This problem is nonconvex and computationally heavy to solve exactly. We adopt a two-step approach to find an approximate solution. In the first step, we construct a polyhedral set in the space of uncertainty that contains enough mass under all distributions in the ambiguity set. This set is constructed by solving several two-dimensional distributionally robust problems. In the second step, we solve a linear robust optimization problem where the uncertain constraint is imposed for all uncertainty values lying in the polyhedral set. We demonstrate the scalability and robustness of our method using numerical experiments.

math.OC↗

arXiv2022

Dynamic interventions with limited knowledge in network games

This paper studies the problem of intervention design for steering the actions of noncooperative players in quadratic network games to the social optimum. The players choose their actions with the aim of maximizing their individual payoff functions, while a central regulator uses interventions to modify their marginal returns and maximize the social welfare function. This work builds on the key observation that the solution to the steering problem depends on the knowledge of the regulator on the players' parameters and the underlying network. We, therefore, consider different scenarios based on limited knowledge and propose suitable static, dynamic and adaptive intervention protocols. We formally prove convergence to the social optimum under the proposed mechanisms. We demonstrate our theoretical findings on a case study of Cournot competition with differentiated goods.

math.OC↗

arXiv2021

Data-driven distributionally robust iterative risk-constrained model predictive control

This paper considers a risk-constrained infinite-horizon optimal control problem and proposes to solve it in an iterative manner. Each iteration of the algorithm generates a trajectory from the starting point to the target equilibrium state by implementing a distributionally robust risk-constrained model predictive control (MPC) scheme. At each iteration, a set of safe states (that satisfy the risk-constraint with high probability) and a certain number of independent and identically distributed samples of the uncertainty governing the risk constraint are available. These states and samples are accumulated in previous iterations. The safe states are used as terminal constraint in the MPC scheme and samples are used to construct a set of distributions, termed ambiguity set, such that it contains the underlying distribution of the uncertainty with high probability. The risk-constraint in each iteration is required to hold for all distributions in the ambiguity set. We establish that the trajectories generated by our iterative procedure are feasible, safe, and converge asymptotically to the equilibrium. Simulation example illustrates our results for the case of finding a risk-constrained path for a mobile robot in the presence of an uncertain obstacle.

math.OC↗

arXiv2021

Steering the aggregative behavior of noncooperative agents: a nudge framework

This paper considers the problem of steering the aggregative behavior of a population of noncooperative price-taking agents towards a desired behavior. Different from conventional pricing schemes where the price is fully available for design, we consider the scenario where a system regulator broadcasts a price prediction signal that can be different from the actual price incurred by the agents. The resulting reliability issues are taken into account by including trust dynamics in our model, implying that the agents will not blindly follow the signal sent by the regulator, but rather follow it based on the history of its accuracy, i.e, its deviation from the actual price. We present several nudge mechanisms to generate suitable price prediction signals that are able to steer the aggregative behavior of the agents to stationary as well as temporal desired aggregative behaviors. We provide analytical convergence guarantees for the resulting multi-components models. In particular, we prove that the proposed nudge mechanisms earn and maintain full trust of the agents, and the aggregative behavior converges to the desired one. The analytical results are complemented by a numerical case study of coordinated charging of plug-in electric vehicles.

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arXiv2020

Consistency of Distributionally Robust Risk- and Chance-Constrained Optimization under Wasserstein Ambiguity Sets

We study stochastic optimization problems with chance and risk constraints, where in the latter, risk is quantified in terms of the conditional value-at-risk (CVaR). We consider the distributionally robust versions of these problems, where the constraints are required to hold for a family of distributions constructed from the observed realizations of the uncertainty via the Wasserstein distance. Our main results establish that if the samples are drawn independently from an underlying distribution and the problems satisfy suitable technical assumptions, then the optimal value and optimizers of the distributionally robust versions of these problems converge to the respective quantities of the original problems, as the sample size increases.

math.OC↗

arXiv2020

Wasserstein Distributionally Robust Look-Ahead Economic Dispatch

We consider the problem of look-ahead economic dispatch (LAED) with uncertain renewable energy generation. The goal of this problem is to minimize the cost of conventional energy generation subject to uncertain operational constraints. The risk of violating these constraints must be below a given threshold for a family of probability distributions with characteristics similar to observed past data or predictions. We present two data-driven approaches based on two novel mathematical reformulations of this distributionally robust decision problem. The first one is a tractable convex program in which the uncertain constraints are defined via the distributionally robust conditional-value-at-risk. The second one is a scalable robust optimization program that yields an approximate distributionally robust chance-constrained LAED. Numerical experiments on the IEEE 39-bus system with real solar production data and forecasts illustrate the effectiveness of these approaches. We discuss how system operators should tune these techniques in order to seek the desired robustness-performance trade-off and we compare their computational scalability.

math.OC↗

arXiv2020

Stochastic approximation of CVaR-based variational inequalities

In this paper we study variational inequalities (VI) defined by the conditional value-at-risk (CVaR) of uncertain functions. We introduce stochastic approximation schemes that employ an empirical estimate of the CVaR at each iteration to solve these VIs. We investigate convergence of these algorithms under various assumptions on the monotonicity of the VI and accuracy of the CVaR estimate. Our first algorithm is shown to converge to the exact solution of the VI when the estimation error of the CVaR becomes progressively smaller along any execution of the algorithm. When the estimation error is nonvanishing, we provide two algorithms that provably converge to a neighborhood of the solution of the VI. For these schemes, under strong monotonicity, we provide an explicit relationship between sample size, estimation error, and the size of the neighborhood to which convergence is achieved. A simulation example illustrates our theoretical findings.

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