arXiv subjects

Mahnoosh Alizadeh

Publications and source records attributed to Mahnoosh Alizadeh.

At least 55 records · Page 3Linked to original sources

arXiv2022

Real-Time Electric Vehicle Smart Charging at Workplaces: A Real-World Case Study

We study a real-time smart charging algorithm for electric vehicles (EVs) at a workplace parking lot in order to minimize electricity cost from time-of-use electricity rates and demand charges while ensuring that the owners of the EVs receive adequate levels of charge. Notably, due to real-world constraints, our algorithm is agnostic to both the state-of-charge and the departure time of the EVs and uses scenario generation to account for each EV's unknown future departure time as well as certainty equivalent control to account for the unknown EV arrivals in the future. Real-world charging data from a Google campus in California allows us to build realistic models of charging demand for each day of the week. We then compare various results from our smart charging algorithm to the status quo for a two week period at a Google parking location.

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arXiv2022

An Online Scheduling Algorithm for a Community Energy Storage System

In this paper, we consider a community energy storage (CES) system that is shared by various electricity consumers who want to charge and discharge the CES throughout a given time span. We study the problem facing the manager of such a CES who must schedule the charging, discharging, and capacity reservations for numerous users. Moreover, we consider the case where requests to charge/discharge the CES arrive in an online fashion and the CES manager must immediately allocate charging power and energy capacity to fulfill the request or reject the request altogether. The objective of the CES manager is to maximize the total value gained by all of the users of the CES while accounting for the operational constraints of the CES. We discuss an algorithm titled \textsc{CommunityEnergyScheduling} that acts as a pricing mechanism based on online primal-dual optimization as a solution to the CES manager's problem. The online algorithm estimates the dual variables (prices) in real-time to allow for requests to be allocated or rejected immediately as they arrive. Furthermore, the proposed method promotes charging and discharging cancellations to reduce the CES's usage at popular times and is able to handle the inherent stochastic nature of the requests to charge/discharge stemming from randomness in users' net load patterns and weather uncertainties. Additionally, we are able to show that the algorithm is able to handle any adversarially chosen request sequence and will always yield total welfare within a factor of 1/a of the offline optimal welfare.

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arXiv2021

Strategically revealing intentions in General Lotto games

Strategic decision-making in uncertain and adversarial environments is crucial for the security of modern systems and infrastructures. A salient feature of many optimal decision-making policies is a level of unpredictability, or randomness, which helps to keep an adversary uncertain about the system's behavior. This paper seeks to explore decision-making policies on the other end of the spectrum -- namely, whether there are benefits in revealing one's strategic intentions to an opponent before engaging in competition. We study these scenarios in a well-studied model of competitive resource allocation problem known as General Lotto games. In the classic formulation, two competing players simultaneously allocate their assets to a set of battlefields, and the resulting payoffs are derived in a zero-sum fashion. Here, we consider a multi-step extension where one of the players has the option to publicly pre-commit assets in a binding fashion to battlefields before play begins. In response, the opponent decides which of these battlefields to secure (or abandon) by matching the pre-commitment with its own assets. They then engage in a General Lotto game over the remaining set of battlefields. Interestingly, this paper highlights many scenarios where strategically revealing intentions can actually significantly improve one's payoff. This runs contrary to the conventional wisdom that randomness should be a central component of decision-making in adversarial environments.

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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.

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arXiv2021

The Division of Assets in Multiagent Systems: A Case Study in Team Blotto Games

Multi-agent systems are designed to concurrently accomplish a diverse set of tasks at unprecedented scale. Here, the central problems faced by a system operator are to decide (i) how to divide available resources amongst the agents assigned to tasks and (ii) how to coordinate the behavior of the agents to optimize the efficiency of the resulting collective behavior. The focus of this paper is on problem (i), where we seek to characterize the impact of the division of resources on the best-case efficiency of the resulting collective behavior. Specifically, we focus on a team Colonel Blotto game where there are two sub-colonels competing against a common adversary in a two battlefield environment. Here, each sub-colonel is assigned a given resource budget and is required to allocate these resources independent of the other sub-colonel. However, their success is dependent on the allocation strategy of both sub-colonels. The central focus of this manuscript is on how to divide a common pool of resources among the two sub-colonels to optimize the resulting best-case efficiency guarantees. Intuitively, one would imagine that the more balanced the division of resources, the worse the performance, as such divisions restrict the sub-colonels' ability to employ joint randomized strategies that tend to be necessary for optimizing performance guarantees. However, the main result of this paper demonstrates that this intuition is actually incorrect. A more balanced division of resources can offer better performance guarantees than a more centralized division. Hence, this paper demonstrates that the resource division problem is highly non-trivial in such enmeshed environments and worthy of significant future research efforts.

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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.

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arXiv2020

The Impact of Complex and Informed Adversarial Behavior in Graphical Coordination Games

How does system-level information impact the ability of an adversary to degrade performance in a networked control system? How does the complexity of an adversary's strategy affect its ability to degrade performance? This paper focuses on these questions in the context of graphical coordination games where an adversary can influence a given fraction of the agents in the system, and the agents follow log-linear learning, a well-known distributed learning algorithm. Focusing on a class of homogeneous ring graphs of various connectivity, we begin by demonstrating that minimally connected ring graphs are the most susceptible to adversarial influence. We then proceed to characterize how both (i) the sophistication of the attack strategies (static vs dynamic) and (ii) the informational awareness about the network structure can be leveraged by an adversary to degrade system performance. Focusing on the set of adversarial policies that induce stochastically stable states, our findings demonstrate that the relative importance between sophistication and information changes depending on the the influencing power of the adversary. In particular, sophistication far outweighs informational awareness with regards to degrading system-level damage when the adversary's influence power is relatively weak. However, the opposite is true when an adversary's influence power is more substantial.

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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.

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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.

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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.

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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.

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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.

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arXiv2020

Regret Bounds for Safe Gaussian Process Bandit Optimization

Many applications require a learner to make sequential decisions given uncertainty regarding both the system's payoff function and safety constraints. In safety-critical systems, it is paramount that the learner's actions do not violate the safety constraints at any stage of the learning process. In this paper, we study a stochastic bandit optimization problem where the unknown payoff and constraint functions are sampled from Gaussian Processes (GPs) first considered in [Srinivas et al., 2010]. We develop a safe variant of GP-UCB called SGP-UCB, with necessary modifications to respect safety constraints at every round. The algorithm has two distinct phases. The first phase seeks to estimate the set of safe actions in the decision set, while the second phase follows the GP-UCB decision rule. Our main contribution is to derive the first sub-linear regret bounds for this problem. We numerically compare SGP-UCB against existing safe Bayesian GP optimization algorithms.

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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.

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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.

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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.

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arXiv2019

Characterizing the interplay between information and strength in Blotto games

In this paper, we investigate informational asymmetries in the Colonel Blotto game, a game-theoretic model of competitive resource allocation between two players over a set of battlefields. The battlefield valuations are subject to randomness. One of the two players knows the valuations with certainty. The other knows only a distribution on the battlefield realizations. However, the informed player has fewer resources to allocate. We characterize unique equilibrium payoffs in a two battlefield setup of the Colonel Blotto game. We then focus on a three battlefield setup in the General Lotto game, a popular variant of the Colonel Blotto game. We characterize the unique equilibrium payoffs and mixed equilibrium strategies. We quantify the value of information - the difference in equilibrium payoff between the asymmetric information game and complete information game. We find information strictly improves the informed player's performance guarantee. However, the magnitude of improvement varies with the informed player's strength as well as the game parameters. Our analysis highlights the interplay between strength and information in adversarial environments.

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arXiv2019

Resilient Distributed Optimization Algorithms for Resource Allocation

Distributed algorithms provide flexibility over centralized algorithms for resource allocation problems, e.g., cyber-physical systems. However, the distributed nature of these algorithms often makes the systems susceptible to man-in-the-middle attacks, especially when messages are transmitted between price-taking agents and a central coordinator. We propose a resilient strategy for distributed algorithms under the framework of primal-dual distributed optimization. We formulate a robust optimization model that accounts for Byzantine attacks on the communication channels between agents and coordinator. We propose a resilient primal-dual algorithm using state-of-the-art robust statistics methods. The proposed algorithm is shown to converge to a neighborhood of the robust optimization model, where the neighborhood's radius is proportional to the fraction of attacked channels.

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