arXiv subjects

Berkay Turan

Publications and source records attributed to Berkay Turan.

13 recordsLinked to original sources

arXiv2023

A Safe First-Order Method for Pricing-Based Resource Allocation in Safety-Critical Networks

We introduce a novel algorithm for solving network utility maximization (NUM) problems that arise in resource allocation schemes over networks with known safety-critical constraints, where the constraints form an arbitrary convex and compact feasible set. Inspired by applications where customers' demand can only be affected through posted prices and real-time two-way communication with customers is not available, we require an algorithm to generate ``safe prices''. This means that at no iteration should the realized demand in response to the posted prices violate the safety constraints of the network. Thus, in contrast to existing distributed first-order methods, our algorithm, called safe pricing for NUM (SPNUM), is guaranteed to produce feasible primal iterates at all iterations. At the heart of the algorithm lie two key steps that must go hand in hand to guarantee safety and convergence: 1) applying a projected gradient method on a shrunk feasible set to get the desired demand, and 2) estimating the price response function of the users and determining the price so that the induced demand is close to the desired demand. We ensure safety by adjusting the shrinkage to account for the error between the induced demand and the desired demand. In addition, by gradually reducing the amount of shrinkage and the step size of the gradient method, we prove that the primal iterates produced by the SPNUM achieve a sublinear static regret of ${\cal O}(\log{(T)})$ after $T$ time steps.

math.OC↗

arXiv2023

Directional Optimism for Safe Linear Bandits

The safe linear bandit problem is a version of the classical stochastic linear bandit problem where the learner's actions must satisfy an uncertain constraint at all rounds. Due its applicability to many real-world settings, this problem has received considerable attention in recent years. By leveraging a novel approach that we call directional optimism, we find that it is possible to achieve improved regret guarantees for both well-separated problem instances and action sets that are finite star convex sets. Furthermore, we propose a novel algorithm for this setting that improves on existing algorithms in terms of empirical performance, while enjoying matching regret guarantees. Lastly, we introduce a generalization of the safe linear bandit setting where the constraints are convex and adapt our algorithms and analyses to this setting by leveraging a novel convex-analysis based approach.

cs.LG↗

arXiv2023

Safe Pricing Mechanisms for Distributed Resource Allocation with Bandit Feedback

In societal-scale infrastructures, such as electric grids or transportation networks, pricing mechanisms are often used as a way to shape users' demand in order to lower operating costs and improve reliability. Existing approaches to pricing design for safety-critical networks often require that users are queried beforehand to negotiate prices, which has proven to be challenging to implement in the real-world. To offer a more practical alternative, we develop learning-based pricing mechanisms that require no input from the users. These pricing mechanisms aim to maximize the utility of the users' consumption by gradually estimating the users' price response over a span of $T$ time steps (e.g., days) while ensuring that the infrastructure network's safety constraints that limit the users' demand are satisfied at all time steps. We propose two different algorithms for the two different scenarios when, 1) the utility function is chosen by the central coordinator to achieve a social objective and 2) the utility function is defined by the price response under the assumption that the users are self-interested agents. We prove that both algorithms enjoy $\tilde{O} (T^{2/3})$ regret with high probability. We then apply these algorithms to demand response pricing for the smart grid and numerically demonstrate their effectiveness.

eess.SY↗

arXiv2023

The Impact of the Geometric Properties of the Constraint Set in Safe Optimization with Bandit Feedback

We consider a safe optimization problem with bandit feedback in which an agent sequentially chooses actions and observes responses from the environment, with the goal of maximizing an arbitrary function of the response while respecting stage-wise constraints. We propose an algorithm for this problem, and study how the geometric properties of the constraint set impact the regret of the algorithm. In order to do so, we introduce the notion of the sharpness of a particular constraint set, which characterizes the difficulty of performing learning within the constraint set in an uncertain setting. This concept of sharpness allows us to identify the class of constraint sets for which the proposed algorithm is guaranteed to enjoy sublinear regret. Simulation results for this algorithm support the sublinear regret bound and provide empirical evidence that the sharpness of the constraint set impacts the performance of the algorithm.

cs.LG↗

arXiv2022

Safe Dual Gradient Method for Network Utility Maximization Problems

In this paper, we introduce a novel first-order dual gradient algorithm for solving network utility maximization problems that arise in resource allocation schemes over networks with safety-critical constraints. Inspired by applications where customers' demand can only be affected through posted prices and real-time two-way communication with customers is not available, we require an algorithm to generate \textit{safe prices}. This means that at no iteration should the realized demand in response to the posted prices violate the safety constraints of the network. Thus, in contrast to existing first-order methods, our algorithm, called the safe dual gradient method (SDGM), is guaranteed to produce feasible primal iterates at all iterations. We ensure primal feasibility by 1) adding a diminishing safety margin to the constraints, and 2) using a sign-based dual update method with different step sizes for plus and minus directions. In addition, we prove that the primal iterates produced by the SDGM achieve a sublinear static regret of ${\cal O}(\sqrt{T})$.

math.OC↗

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

Robust Distributed Optimization With Randomly Corrupted Gradients

In this paper, we propose a first-order distributed optimization algorithm that is provably robust to Byzantine failures-arbitrary and potentially adversarial behavior, where all the participating agents are prone to failure. We model each agent's state over time as a two-state Markov chain that indicates Byzantine or trustworthy behaviors at different time instants. We set no restrictions on the maximum number of Byzantine agents at any given time. We design our method based on three layers of defense: 1) temporal robust aggregation, 2) spatial robust aggregation, and 3) gradient normalization. We study two settings for stochastic optimization, namely Sample Average Approximation and Stochastic Approximation. We provide convergence guarantees of our method for strongly convex and smooth non-convex cost functions.

math.OC↗

arXiv2021

Competition in Electric Autonomous Mobility on Demand Systems

This paper investigates the impacts of competition in autonomous mobility-on-demand systems. By adopting a network-flow based formulation, we first determine the optimal strategies of profit-maximizing platform operators in monopoly and duopoly markets, including the optimal prices of rides. Furthermore, we characterize the platform operator's profits and the consumer surplus. We show that for the duopoly, the equilibrium prices for rides have to be symmetric between the firms. Then, in order to study the benefits of introducing competition in the market, we derive universal theoretical bounds on the ratio of prices for rides, aggregate demand served, profits of the firms, and consumer surplus between the monopolistic and the duopolistic setting. We discuss how consumers' firm loyalty affects each of the aforementioned metrics. Finally, using the Manhattan network and demand data, we quantify the efficacy of static pricing and routing policies and compare it to real-time model predictive policies.

math.OC↗

arXiv2021

On Robustness of the Normalized Subgradient Method with Randomly Corrupted Subgradients

Numerous modern optimization and machine learning algorithms rely on subgradient information being trustworthy and hence, they may fail to converge when such information is corrupted. In this paper, we consider the setting where subgradient information may be arbitrarily corrupted (with a given probability) and study the robustness properties of the normalized subgradient method. Under the probabilistic corruption scenario, we prove that the normalized subgradient method, whose updates rely solely on directional information of the subgradient, converges to a minimizer for convex, strongly convex, and weakly-pseudo convex functions satisfying certain conditions. Numerical evidence on linear regression and logistic classification problems support our results.

math.OC↗

arXiv2020

Dynamic Pricing and Fleet Management for Electric Autonomous Mobility on Demand Systems

The proliferation of ride sharing systems is a major drive in the advancement of autonomous and electric vehicle technologies. This paper considers the joint routing, battery charging, and pricing problem faced by a profit-maximizing transportation service provider that operates a fleet of autonomous electric vehicles. We first establish the static planning problem by considering time-invariant system parameters and determine the optimal static policy. While the static policy provides stability of customer queues waiting for rides even if consider the system dynamics, we see that it is inefficient to utilize a static policy as it can lead to long wait times for customers and low profits. To accommodate for the stochastic nature of trip demands, renewable energy availability, and electricity prices and to further optimally manage the autonomous fleet given the need to generate integer allocations, a real-time policy is required. The optimal real-time policy that executes actions based on full state information of the system is the solution of a complex dynamic program. However, we argue that it is intractable to exactly solve for the optimal policy using exact dynamic programming methods and therefore apply deep reinforcement learning to develop a near-optimal control policy. The two case studies we conducted in Manhattan and San Francisco demonstrate the efficacy of our real-time policy in terms of network stability and profits, while keeping the queue lengths up to 200 times less than the static policy.

eess.SY↗

arXiv2020

Resilient Primal-Dual Optimization Algorithms for Distributed Resource Allocation

Distributed algorithms for multi-agent resource allocation can provide privacy and scalability over centralized algorithms in many cyber-physical systems. However, the distributed nature of these algorithms can render these systems vulnerable to man-in-the-middle attacks that can lead to non-convergence and infeasibility of resource allocation schemes. In this paper, we propose attack-resilient distributed algorithms based on primal-dual optimization when Byzantine attackers are present in the system. In particular, we design attack-resilient primal-dual algorithms for static and dynamic impersonation attacks by means of robust statistics. For static impersonation attacks, we formulate a robustified optimization model and show that our algorithm guarantees convergence to a neighborhood of the optimal solution of the robustified problem. On the other hand, a robust optimization model is not required for the dynamic impersonation attack scenario and we are able to design an algorithm that is shown to converge to a near-optimal solution of the original problem. We analyze the performances of our algorithms through both theoretical and computational studies.

math.OC↗

arXiv2019

Smart Charging Benefits in Autonomous Mobility on Demand Systems

In this paper, we study the potential benefits from smart charging for a fleet of electric vehicles (EVs) providing autonomous mobility-on-demand (AMoD) services. We first consider a profit-maximizing platform operator who makes decisions for routing, charging, rebalancing, and pricing for rides based on a network flow model. Clearly, each of these decisions directly influence the fleet's smart charging potential; however, it is not possible to directly characterize the effects of various system parameters on smart charging under a classical network flow model. As such, we propose a modeling variation that allows us to decouple the charging and routing problems faced by the operator. This variation allows us to provide closed-form mathematical expressions relating the charging costs to the maximum battery capacity of the vehicles as well as the fleet operational costs. We show that investing in larger battery capacities and operating more vehicles for rebalancing reduces the charging costs, while increasing the fleet operational costs. Hence, we study the trade-off the operator faces, analyze the minimum cost fleet charging strategy, and provide numerical results illustrating the smart charging benefits to the operator.

eess.SY↗

arXiv2019

Online Charge Scheduling for Electric Vehicles in Autonomous Mobility on Demand Fleets

In this paper, we study an online charge scheduling strategy for fleets of autonomous-mobility-on-demand electric vechicles (AMoD EVs). We consider the case where vehicles complete trips and then enter a between-ride state throughout the day, with their information becoming available to the fleet operator in an online fashion. In the between-ride state, the vehicles must be scheduled for charging and then routed to their next passenger pick-up locations. Additionally, due to the unknown daily sequences of ride requests, the problem cannot be solved by any offline approach. As such, we study an online welfare maximization heuristic based on primal-dual methods that allocates limited fleet charging resources and rebalances the vehicles while avoiding congestion at charging facilities and pick-up locations. We discuss a competitive ratio result comparing the performance of our online solution to the clairvoyant offline solution and provide numerical results highlighting the performance of our heuristic.

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