arXiv subjects

S. Rasoul Etesami

Publications and source records attributed to S. Rasoul Etesami.

44 records · Page 3Linked to original sources

arXiv2020

Optimal Online Algorithms for File-Bundle Caching and Generalization to Distributed Caching

We consider a generalization of the standard cache problem called file-bundle caching, where different queries (tasks), each containing $l\ge 1$ files, sequentially arrive. An online algorithm that does not know the sequence of queries ahead of time must adaptively decide on what files to keep in the cache to incur the minimum number of cache misses. Here a cache miss refers to the case where at least one file in a query is missing among the cache files. In the special case where $l=1$, this problem reduces to the standard cache problem. We first analyze the performance of the classic least recently used (LRU) algorithm in this setting and show that LRU is a near-optimal online deterministic algorithm for file-bundle caching with regard to competitive ratio. We then extend our results to a generalized $(h,k)$-paging problem in this file-bundle setting, where the performance of the online algorithm with a cache size $k$ is compared to an optimal offline benchmark of a smaller cache size $h<k$. In this latter case, we provide a randomized $O(l \ln \frac{k}{k-h})$-competitive algorithm for our generalized $(h,k)$-paging problem, which can be viewed as an extension of the classic marking algorithm. We complete this result by providing a matching lower bound for the competitive ratio, indicating that the performance of this modified marking algorithm is within a factor of two of any randomized online algorithm. Finally, we look at the distributed version of the file-bundle caching problem where there are $m\ge 1$ identical caches in the system. In this case we show that for $m=l+1$ caches, there is a deterministic distributed caching algorithm which is $(l^2+l)$-competitive and a randomized distributed caching algorithm which is $O(l\ln(2l+1))$-competitive when $l\ge 2$.

cs.DS↗

arXiv2020

Communication-efficient Decentralized Local SGD over Undirected Networks

We consider the distributed learning problem where a network of $n$ agents seeks to minimize a global function $F$. Agents have access to $F$ through noisy gradients, and they can locally communicate with their neighbors a network. We study the Decentralized Local SDG method, where agents perform a number of local gradient steps and occasionally exchange information with their neighbors. Previous algorithmic analysis efforts have focused on the specific network topology (star topology) where a leader node aggregates all agents' information. We generalize that setting to an arbitrary network by analyzing the trade-off between the number of communication rounds and the computational effort of each agent. We bound the expected optimality gap in terms of the number of iterates $T$, the number of workers $n$, and the spectral gap of the underlying network. Our main results show that by using only $R=Ω(n)$ communication rounds, one can achieve an error that scales as $O({1}/{nT})$, where the number of communication rounds is independent of $T$ and only depends on the number of agents. Finally, we provide numerical evidence of our theoretical results through experiments on real and synthetic data.

cs.LG↗

arXiv2020

Toward Optimal Adversarial Policies in the Multiplicative Learning System with a Malicious Expert

We consider a learning system based on the conventional multiplicative weight (MW) rule that combines experts' advice to predict a sequence of true outcomes. It is assumed that one of the experts is malicious and aims to impose the maximum loss on the system. The loss of the system is naturally defined to be the aggregate absolute difference between the sequence of predicted outcomes and the true outcomes. We consider this problem under both offline and online settings. In the offline setting where the malicious expert must choose its entire sequence of decisions a priori, we show somewhat surprisingly that a simple greedy policy of always reporting false prediction is asymptotically optimal with an approximation ratio of $1+O(\sqrt{\frac{\ln N}{N}})$, where $N$ is the total number of prediction stages. In particular, we describe a policy that closely resembles the structure of the optimal offline policy. For the online setting where the malicious expert can adaptively make its decisions, we show that the optimal online policy can be efficiently computed by solving a dynamic program in $O(N^3)$. Our results provide a new direction for vulnerability assessment of commonly used learning algorithms to adversarial attacks where the threat is an integral part of the system.

cs.LG↗

arXiv2020

Duality and Stability in Complex Multiagent State-Dependent Network Dynamics

Despite significant progress on stability analysis of conventional multiagent networked systems with weakly coupled state-network dynamics, most of the existing results have shortcomings in addressing multiagent systems with highly coupled state-network dynamics. Motivated by numerous applications of such dynamics, in our previous work [1], we initiated a new direction for stability analysis of such systems that uses a sequential optimization framework. Building upon that, in this paper, we extend our results by providing another angle on multiagent network dynamics from a duality perspective, which allows us to view the network structure as dual variables of a constrained nonlinear program. Leveraging that idea, we show that the evolution of the coupled state-network multiagent dynamics can be viewed as iterates of a primal-dual algorithm for a static constrained optimization/saddle-point problem. This view bridges the Lyapunov stability of state-dependent network dynamics and frequently used optimization techniques such as block coordinated descent, mirror descent, the Newton method, and the subgradient method. As a result, we develop a systematic framework for analyzing the Lyapunov stability of state-dependent network dynamics using techniques from nonlinear optimization. Finally, we support our theoretical results through numerical simulations from social science.

eess.SY↗

arXiv2020

Optimal versus Nash Equilibrium Computation for Networked Resource Allocation

Motivated by emerging resource allocation and data placement problems such as web caches and peer-to-peer systems, we consider and study a class of resource allocation problems over a network of agents (nodes). In this model, nodes can store only a limited number of resources while accessing the remaining ones through their closest neighbors. We consider this problem under both optimization and game-theoretic frameworks. In the case of optimal resource allocation we will first show that when there are only k=2 resources, the optimal allocation can be found efficiently in O(n^2\log n) steps, where n denotes the total number of nodes. However, for k>2 this problem becomes NP-hard with no polynomial time approximation algorithm with a performance guarantee better than 1+1/102k^2, even under metric access costs. We then provide a 3-approximation algorithm for the optimal resource allocation which runs only in linear time O(n). Subsequently, we look at this problem under a selfish setting formulated as a noncooperative game and provide a 3-approximation algorithm for obtaining its pure Nash equilibria under metric access costs. We then establish an equivalence between the set of pure Nash equilibria and flip-optimal solutions of the Max-k-Cut problem over a specific weighted complete graph. Using this reduction, we show that finding the lexicographically smallest Nash equilibrium for k> 2 is NP-hard, and provide an algorithm to find it in O(n^3 2^n) steps. While the reduction to weighted Max-k-Cut suggests that finding a pure Nash equilibrium using best response dynamics might be PLS-hard, it allows us to use tools from quadratic programming to devise more systematic algorithms towards obtaining Nash equilibrium points.

cs.GT↗

arXiv2019

Smart Routing of Electric Vehicles for Load Balancing in Smart Grids

Electric vehicles (EVs) are expected to be a major component of the smart grid. The rapid proliferation of EVs will introduce an unprecedented load on the existing electric grid due to the charging/discharging behavior of the EVs, thus motivating the need for novel approaches for routing EVs across the grid. In this paper, a novel gametheoretic framework for smart routing of EVs within the smart grid is proposed. The goal of this framework is to balance the electricity load across the grid while taking into account the traffic congestion and the waiting time at charging stations. The EV routing problem is formulated as a noncooperative game. For this game, it is shown that selfish behavior of EVs will result in a pure-strategy Nash equilibrium with the price of anarchy upper bounded by the variance of the ground load induced by the residential, industrial, or commercial users. Moreover, the results are extended to capture the stochastic nature of induced ground load as well as the subjective behavior of the owners of EVs as captured by using notions from the behavioral framework of prospect theory. Simulation results provide new insights on more efficient energy pricing at charging stations and under more realistic grid conditions.

cs.GT↗

arXiv2018

A Simple Framework for Stability Analysis of State-Dependent Networks of Heterogeneous Agents

Stability and analysis of multi-agent network systems with state-dependent switching typologies have been a fundamental and longstanding challenge in control, social sciences, and many other related fields. These already complex systems become further complicated once one accounts for asymmetry or heterogeneity of the underlying agents/dynamics. Despite extensive progress in analysis of conventional networked decision systems where the network evolution and state dynamics are driven by independent or weakly coupled processes, most of the existing results fail to address multi-agent systems where the network and state dynamics are highly coupled and evolve based on status of heterogeneous agents. Motivated by numerous applications of such dynamics in social sciences, in this paper we provide a new direction toward analysis of dynamic networks of heterogeneous agents under complex time-varying environments. As a result we show how Lyapunov stability of several challenging problems from opinion dynamics can be established using a simple application of our framework. Moreover, we introduce a new class of asymmetric opinion dynamics, namely nearest neighbor dynamics, and show how our approach can be used to analyze their behavior. In particular, we extend our results to game-theoretic settings and provide new insights toward analysis of complex networked multi-agent systems using exciting field of sequential optimization.

eess.SY↗

arXiv2017

Managing Price Uncertainty in Prosumer-Centric Energy Trading: A Prospect-Theoretic Stackelberg Game Approach

In this paper, the problem of energy trading between smart grid prosumers, who can simultaneously consume and produce energy, and a grid power company is studied. The problem is formulated as a single-leader, multiple-follower Stackelberg game between the power company and multiple prosumers. In this game, the power company acts as a leader who determines the pricing strategy that maximizes its profits, while the prosumers act as followers who react by choosing the amount of energy to buy or sell so as to optimize their current and future profits. The proposed game accounts for each prosumer's subjective decision when faced with the uncertainty of profits, induced by the random future price. In particular, the framing effect, from the framework of prospect theory (PT), is used to account for each prosumer's valuation of its gains and losses with respect to an individual utility reference point. The reference point changes between prosumers and stems from their past experience and future aspirations of profits. The followers' noncooperative game is shown to admit a unique pure-strategy Nash equilibrium (NE) under classical game theory (CGT) which is obtained using a fully distributed algorithm. The results are extended to account for the case of PT using algorithmic solutions that can achieve an NE under certain conditions. Simulation results show that the total grid load varies significantly with the prosumers' reference point and their loss-aversion level. In addition, it is shown that the power company's profits considerably decrease when it fails to account for the prosumers' subjective perceptions under PT.

cs.GT↗