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S. Rasoul Etesami

Publications and source records attributed to S. Rasoul Etesami.

At least 37 records · Page 2Linked to original sources
arXiv2024

Learning How to Strategically Disclose Information

Strategic information disclosure, in its simplest form, considers a game between an information provider (sender) who has access to some private information that an information receiver is interested in. While the receiver takes an action that affects the utilities of both players, the sender can design information (or modify beliefs) of the receiver through signal commitment, hence posing a Stackelberg game. However, obtaining a Stackelberg equilibrium for this game traditionally requires the sender to have access to the receiver's objective. In this work, we consider an online version of information design where a sender interacts with a receiver of an unknown type who is adversarially chosen at each round. Restricting attention to Gaussian prior and quadratic costs for the sender and the receiver, we show that $\mathcal{O}(\sqrt{T})$ regret is achievable with full information feedback, where $T$ is the total number of interactions between the sender and the receiver. Further, we propose a novel parametrization that allows the sender to achieve $\mathcal{O}(\sqrt{T})$ regret for a general convex utility function. We then consider the Bayesian Persuasion problem with an additional cost term in the objective function, which penalizes signaling policies that are more informative and obtain $\mathcal{O}(\log(T))$ regret. Finally, we establish a sublinear regret bound for the partial information feedback setting and provide simulations to support our theoretical results.

cs.GT↗
arXiv2024

Online Reinforcement Learning in Markov Decision Process Using Linear Programming

We consider online reinforcement learning in episodic Markov decision process (MDP) with unknown transition function and stochastic rewards drawn from some fixed but unknown distribution. The learner aims to learn the optimal policy and minimize their regret over a finite time horizon through interacting with the environment. We devise a simple and efficient model-based algorithm that achieves $\widetilde{O}(LX\sqrt{TA})$ regret with high probability, where $L$ is the episode length, $T$ is the number of episodes, and $X$ and $A$ are the cardinalities of the state space and the action space, respectively. The proposed algorithm, which is based on the concept of ``optimism in the face of uncertainty", maintains confidence sets of transition and reward functions and uses occupancy measures to connect the online MDP with linear programming. It achieves a tighter regret bound compared to the existing works that use a similar confidence set framework and improves computational effort compared to those that use a different framework but with a slightly tighter regret bound.

cs.LG↗
arXiv2024

Local Environment Poisoning Attacks on Federated Reinforcement Learning

Federated learning (FL) has become a popular tool for solving traditional Reinforcement Learning (RL) tasks. The multi-agent structure addresses the major concern of data-hungry in traditional RL, while the federated mechanism protects the data privacy of individual agents. However, the federated mechanism also exposes the system to poisoning by malicious agents that can mislead the trained policy. Despite the advantage brought by FL, the vulnerability of Federated Reinforcement Learning (FRL) has not been well-studied before. In this work, we propose a general framework to characterize FRL poisoning as an optimization problem and design a poisoning protocol that can be applied to policy-based FRL. Our framework can also be extended to FRL with actor-critic as a local RL algorithm by training a pair of private and public critics. We provably show that our method can strictly hurt the global objective. We verify our poisoning effectiveness by conducting extensive experiments targeting mainstream RL algorithms and over various RL OpenAI Gym environments covering a wide range of difficulty levels. Within these experiments, we compare clean and baseline poisoning methods against our proposed framework. The results show that the proposed framework is successful in poisoning FRL systems and reducing performance across various environments and does so more effectively than baseline methods. Our work provides new insights into the vulnerability of FL in RL training and poses new challenges for designing robust FRL algorithms

cs.LG↗
arXiv2023

Scalable and Independent Learning of Nash Equilibrium Policies in $n$-Player Stochastic Games with Unknown Independent Chains

We study a subclass of $n$-player stochastic games, namely, stochastic games with independent chains and unknown transition matrices. In this class of games, players control their own internal Markov chains whose transitions do not depend on the states/actions of other players. However, players' decisions are coupled through their payoff functions. We assume players can receive only realizations of their payoffs, and that the players can not observe the states and actions of other players, nor do they know the transition probability matrices of their own Markov chain. Relying on a compact dual formulation of the game based on occupancy measures and the technique of confidence set to maintain high-probability estimates of the unknown transition matrices, we propose a fully decentralized mirror descent algorithm to learn an $ε$-NE for this class of games. The proposed algorithm has the desired properties of independence, scalability, and convergence. Specifically, under no assumptions on the reward functions, we show the proposed algorithm converges in polynomial time in a weaker distance (namely, the averaged Nikaido-Isoda gap) to the set of $ε$-NE policies with arbitrarily high probability. Moreover, assuming the existence of a variationally stable Nash equilibrium policy, we show that the proposed algorithm converges asymptotically to the stable $ε$-NE policy with arbitrarily high probability. In addition to Markov potential games and linear-quadratic stochastic games, this work provides another subclass of $n$-player stochastic games that, under some mild assumptions, admit polynomial-time learning algorithms for finding their stationary $ε$-NE policies.

cs.GT↗
arXiv2023

Limited-Trust in Diffusion of Competing Alternatives over Social Networks

We consider the diffusion of two alternatives in social networks using a game-theoretic approach. Each individual plays a coordination game with its neighbors repeatedly and decides which to adopt. As products are used in conjunction with others and through repeated interactions, individuals are more interested in their long-term benefits and tend to show trust to others to maximize their long-term utility by choosing a suboptimal option with respect to instantaneous payoff. To capture such trust behavior, we deploy limited-trust equilibrium (LTE) in diffusion process. We analyze the convergence of emerging dynamics to equilibrium points using mean-field approximation and study the equilibrium state and the convergence rate of diffusion using absorption probability and expected absorption time of a reduced-size absorbing Markov chain. We also show that the diffusion model on LTE under the best-response strategy can be converted to the well-known linear threshold model. Simulation results show that when agents behave trustworthy, their long-term utility will increase significantly compared to the case when they are solely self-interested. Moreover, the Markov chain analysis provides a good estimate of convergence properties over random networks.

cs.SI↗
arXiv2023

Online and Offline Dynamic Influence Maximization Games Over Social Networks

In this work, we consider dynamic influence maximization games over social networks with multiple players (influencers). The goal of each influencer is to maximize their own reward subject to their limited total budget rate constraints. Thus, influencers need to carefully design their investment policies considering individuals' opinion dynamics and other influencers' investment strategies, leading to a dynamic game problem. We first consider the case of a single influencer who wants to maximize its utility subject to a total budget rate constraint. We study both offline and online versions of the problem where the opinion dynamics are either known or not known a priori. In the singe-influencer case, we propose an online no-regret algorithm, meaning that as the number of campaign opportunities grows, the average utilities obtained by the offline and online solutions converge. Then, we consider the game formulation with multiple influencers in offline and online settings. For the offline setting, we show that the dynamic game admits a unique Nash equilibrium policy and provide a method to compute it. For the online setting and with two influencers, we show that if each influencer applies the same no-regret online algorithm proposed for the single-influencer maximization problem, they will converge to the set of $ε$-Nash equilibrium policies where $ε=O(\frac{1}{\sqrt{K}})$ scales in average inversely with the number of campaign times $K$ considering the average utilities of the influencers. Moreover, we extend this result to any finite number of influencers under more strict requirements on the information structure. Finally, we provide numerical analysis to validate our results under various settings.

cs.GT↗
arXiv2023

Maximizing Social Welfare Subject to Network Externalities: A Unifying Submodular Optimization Approach

We consider the problem of allocating multiple indivisible items to a set of networked agents to maximize the social welfare subject to network externalities. Here, the social welfare is given by the sum of agents' utilities and externalities capture the effect that one user of an item has on the item's value to others. We first provide a general formulation that captures some of the existing models as a special case. We then show that the social welfare maximization problem benefits some nice diminishing or increasing marginal return properties. That allows us to devise polynomial-time approximation algorithms using the Lovasz extension and multilinear extension of the objective functions. Our principled approach recovers or improves some of the existing algorithms and provides a simple and unifying framework for maximizing social welfare subject to network externalities.

cs.GT↗
arXiv2023

Online Learning in Budget-Constrained Dynamic Colonel Blotto Games

In this paper, we study the strategic allocation of limited resources using a Colonel Blotto game (CBG) under a dynamic setting and analyze the problem using an online learning approach. In this model, one of the players is a learner who has limited troops to allocate over a finite time horizon, and the other player is an adversary. In each round, the learner plays a one-shot Colonel Blotto game with the adversary and strategically determines the allocation of troops among battlefields based on past observations. The adversary chooses its allocation action randomly from some fixed distribution that is unknown to the learner. The learner's objective is to minimize its regret, which is the difference between the cumulative reward of the best mixed strategy and the realized cumulative reward by following a learning algorithm while not violating the budget constraint. The learning in dynamic CBG is analyzed under the framework of combinatorial bandits and bandits with knapsacks. We first convert the budget-constrained dynamic CBG to a path planning problem on a directed graph. We then devise an efficient algorithm that combines a special combinatorial bandit algorithm for path planning problem and a bandits with knapsack algorithm to cope with the budget constraint. The theoretical analysis shows that the learner's regret is bounded by a term sublinear in time horizon and polynomial in other parameters. Finally, we justify our theoretical results by carrying out simulations for various scenarios.

cs.LG↗
arXiv2023

Robustness of Dynamics in Games: A Contraction Mapping Decomposition Approach

A systematic framework for analyzing dynamical attributes of games has not been well-studied except for the special class of potential or near-potential games. In particular, the existing results have shortcomings in determining the asymptotic behavior of a given dynamic in a designated game. Although there is a large body literature on developing convergent dynamics to the Nash equilibrium (NE) of a game, in general, the asymptotic behavior of an underlying dynamic may not be even close to a NE. In this paper, we initiate a new direction towards game dynamics by studying the fundamental properties of the map of dynamics in games. To this aim, we first decompose the map of a given dynamic into contractive and non-contractive parts and then explore the asymptotic behavior of those dynamics using the proximity of such decomposition to contraction mappings. In particular, we analyze the non-contractive behavior for better/best response dynamics in discrete-action space sequential/repeated games and show that the non-contractive part of those dynamics is well-behaved in a certain sense. That allows us to estimate the asymptotic behavior of such dynamics using a neighborhood around the fixed point of their contractive part proxy. Finally, we demonstrate the practicality of our framework via an example from duopoly Cournot games.

cs.GT↗
arXiv2023

Learning Stationary Nash Equilibrium Policies in $n$-Player Stochastic Games with Independent Chains

We consider a subclass of $n$-player stochastic games, in which players have their own internal state/action spaces while they are coupled through their payoff functions. It is assumed that players' internal chains are driven by independent transition probabilities. Moreover, players can receive only realizations of their payoffs, not the actual functions, and cannot observe each other's states/actions. For this class of games, we first show that finding a stationary Nash equilibrium (NE) policy without any assumption on the reward functions is interactable. However, for general reward functions, we develop polynomial-time learning algorithms based on dual averaging and dual mirror descent, which converge in terms of the averaged Nikaido-Isoda distance to the set of $ε$-NE policies almost surely or in expectation. In particular, under extra assumptions on the reward functions such as social concavity, we derive polynomial upper bounds on the number of iterates to achieve an $ε$-NE policy with high probability. Finally, we evaluate the effectiveness of the proposed algorithms in learning $ε$-NE policies using numerical experiments for energy management in smart grids.

cs.LG↗
arXiv2022

Distributed Computation for the Non-metric Data Placement Problem using Glauber Dynamics and Auctions

We consider the non-metric data placement problem and develop distributed algorithms for computing or approximating its optimal integral solution. We first show that the non-metric data placement problem is inapproximable up to a logarithmic factor. We then provide a game-theoretic decomposition of the objective function and show that natural Glauber dynamics in which players update their resources with probability proportional to the utility they receive from caching those resources will converge to an optimal global solution for a sufficiently large noise parameter. In particular, we establish the polynomial mixing time of the Glauber dynamics for a certain range of noise parameters. Finally, we provide another auction-based distributed algorithm, which allows us to approximate the optimal global solution with a performance guarantee that depends on the ratio of the revenue vs. social welfare obtained from the underlying auction. Our results provide the first distributed computation algorithms for the non-metric data placement problem.

cs.GT↗
arXiv2022

The Role of Local Steps in Local SGD

We consider the distributed stochastic optimization problem where $n$ agents want to minimize a global function given by the sum of agents' local functions, and focus on the heterogeneous setting when agents' local functions are defined over non-i.i.d. data sets. We study the Local SGD method, where agents perform a number of local stochastic gradient steps and occasionally communicate with a central node to improve their local optimization tasks. We analyze the effect of local steps on the convergence rate and the communication complexity of Local SGD. In particular, instead of assuming a fixed number of local steps across all communication rounds, we allow the number of local steps during the $i$-th communication round, $H_i$, to be different and arbitrary numbers. Our main contribution is to characterize the convergence rate of Local SGD as a function of $\{H_i\}_{i=1}^R$ under various settings of strongly convex, convex, and nonconvex local functions, where $R$ is the total number of communication rounds. Based on this characterization, we provide sufficient conditions on the sequence $\{H_i\}_{i=1}^R$ such that Local SGD can achieve linear speed-up with respect to the number of workers. Furthermore, we propose a new communication strategy with increasing local steps superior to existing communication strategies for strongly convex local functions. On the other hand, for convex and nonconvex local functions, we argue that fixed local steps are the best communication strategy for Local SGD and recover state-of-the-art convergence rate results. Finally, we justify our theoretical results through extensive numerical experiments.

cs.LG↗
arXiv2022

Maximizing Convergence Time in Network Averaging Dynamics Subject to Edge Removal

We consider the consensus interdiction problem (CIP), in which the goal is to maximize the convergence time of consensus averaging dynamics subject to removing a limited number of network edges. We first show that CIP can be cast as an effective resistance interdiction problem (ERIP), in which the goal is to remove a limited number of network edges to maximize the effective resistance between a source node and a sink node. We show that ERIP is strongly NP-hard, even for bipartite graphs of diameter three with fixed source/sink edges, and establish the same hardness result for the CIP. We then show that both ERIP and CIP cannot be approximated up to a (nearly) polynomial factor assuming exponential time hypothesis. Subsequently, we devise a polynomial-time $mn$-approximation algorithm for the ERIP that only depends on the number of nodes $n$ and the number of edges $m$, but is independent of the size of edge resistances. Finally, using a quadratic program formulation for the CIP, we devise an iterative approximation algorithm to find a first-order stationary solution for the CIP and evaluate its good performance through numerical results.

eess.SY↗
arXiv2022

The Role of Gossiping for Information Dissemination over Networked Agents

We consider information dissemination over a network of gossiping agents (nodes). In this model, a source keeps the most up-to-date information about a time-varying binary state of the world, and $n$ receiver nodes want to follow the information at the source as accurately as possible. When the information at the source changes, the source first sends updates to a subset of $m\leq n$ nodes. After that, the nodes share their local information during the gossiping period to disseminate the information further. The nodes then estimate the information at the source using the majority rule at the end of the gossiping period. To analyze information dissemination, we introduce a new error metric to find the average percentage of nodes that can accurately obtain the most up-to-date information at the source. We characterize the equations necessary to obtain the steady-state distribution for the average error and then analyze the system behavior under both high and low gossip rates. In the high gossip rate, in which each node can access other nodes' information more frequently, we show that the nodes update their information based on the majority of the information in the network. In the low gossip rate, we introduce and analyze the gossip gain, which is the reduction at the average error due to gossiping. In particular, we develop an adaptive policy that the source can use to determine its current transmission capacity $m$ based on its past transmission rates and the accuracy of the information at the nodes. In numerical results, we show that when the source's transmission capacity $m$ is limited, gossiping can be harmful as it causes incorrect information to disseminate. We then find the optimal gossip rates to minimize the average error for a fixed $m$. Finally, we illustrate the outperformance of our adaptive policy compared to the constant $m$-selection policy even for the high gossip rates.

cs.IT↗
arXiv2021

Online Assortment and Market Segmentation under Bertrand Competition with Set-Dependent Revenues

We consider an online assortment problem with $[n]:=\{1,2,\ldots,n\}$ sellers, each holding exactly one item $i\in[n]$ with initial inventory $c_i\in \mathbb{Z}_+$, and a sequence of homogeneous buyers arriving over a finite time horizon $t=1,2,\ldots,m$. There is an online platform whose goal is to offer a subset $S_t\subseteq [n]$ of sellers to the arriving buyer at time $t$ to maximize the expected revenue derived over the entire horizon while respecting the inventory constraints. Given an assortment $S_t$ at time $t$, it is assumed that the buyer will select an item from $S_t$ based on the well-known multinomial logit model, a well-justified choice model from the economic literature. In this model, the revenue obtained from selling an item $i$ at a given time $t$ critically depends on the assortment $S_t$ offered at that time and is given by the Nash equilibrium of a Bertrand game among the sellers in $S_t$. This imposes a strong dependence/externality among the offered assortments, sellers' revenues, and inventory levels. Despite that challenge, we devise a constant competitive algorithm for the online assortment problem with homogeneous buyers. We also show that the online assortment problem with heterogeneous buyers does not admit a constant competitive algorithm. To compensate for that issue, we then consider the assortment problem under an offline setting with heterogeneous buyers. Under a mild market consistency assumption, we show that the generalized Bertrand game admits a pure Nash equilibrium over general buyer-seller bipartite graphs. Finally, we develop an $O(\ln m)$-approximation algorithm for optimal market segmentation of the generalized Bertrand game which allows the platform to derive higher revenues by partitioning the market into smaller pools.

cs.GT↗
arXiv2021

Open-Loop Equilibrium Strategies for Dynamic Influence Maximization Game Over Social Networks

We consider the problem of budget allocation for competitive influence maximization over social networks. In this problem, multiple competing parties (players) want to distribute their limited advertising resources over a set of social individuals to maximize their long-run cumulative payoffs. It is assumed that the individuals are connected via a social network and update their opinions based on the classical DeGroot model. The players must decide the budget distribution among the individuals at a finite number of campaign times to maximize their overall payoff given as a function of individuals' opinions. We show that i) the optimal investment strategy for the case of a single-player can be found in polynomial time by solving a concave program, and ii) the open-loop equilibrium strategies for the multiplayer dynamic game can be computed efficiently by following natural regret minimization dynamics. Our results extend the earlier work on the static version of the problem to a dynamic multistage game.

cs.GT↗
arXiv2021

Partisan Confidence Model for Group Polarization

Models of opinion dynamics play a major role in various disciplines, including economics, political science, psychology, and social science, as they provide a framework for analysis and intervention. In spite of the numerous mathematical models of social learning proposed in the literature, only a few models have focused on or allow for the possibility of popular extreme beliefs' formation in a population. This paper closes this gap by introducing the Partisan Confidence (PC) model inspired by the foundations of the well-established socio-psychological theory of groupthink. The model hints at the existence of a tipping point, passing which the opinions of the individuals within a so-called "social bubble" are exaggerated towards an extreme position, no matter how the general population is united or divided. The results are also justified through numerical experiments, which provide new insights into the evolution of opinions and the groupthink phenomenon.

physics.soc-ph↗
arXiv2021

An Optimal Control Framework for Online Job Scheduling with General Cost Functions

We consider the problem of online job scheduling on a single machine or multiple unrelated machines with general job/machine-dependent cost functions. In this model, each job $j$ has a processing requirement (length) $v_{ij}$ and arrives with a nonnegative nondecreasing cost function $g_{ij}(t)$ if it has been dispatched to machine $i$, and this information is revealed to the system upon arrival of job $j$ at time $r_j$. The goal is to dispatch the jobs to the machines in an online fashion and process them preemptively on the machines so as to minimize the generalized completion time $\sum_{j}g_{i(j)j}(C_j)$. Here $i(j)$ refers to the machine to which job $j$ is dispatched, and $C_j$ is the completion time of job $j$ on that machine. It is assumed that jobs cannot migrate between machines and that each machine can work on a single job at any time instance. In particular, we are interested in finding an online scheduling policy whose objective cost is competitive with respect to a slower optimal offline benchmark, i.e., the one that knows all the job specifications a priori and is slower than the online algorithm. We first show that for the case of a single machine and special cost functions $g_j(t)=w_jg(t)$, with nonnegative nondecreasing $g(t)$, the highest-density-first rule is optimal for the generalized fractional completion time. We then extend this result by giving a speed-augmented competitive algorithm for the general nondecreasing cost functions $g_j(t)$ by utilizing a novel optimal control framework. This approach provides a principled method for identifying dual variables in different settings of online job scheduling with general cost functions. Using this method, we also provide a speed-augmented competitive algorithm for multiple unrelated machines with convex functions $g_{ij}(t)$, where the competitive ratio depends on the curvature of cost functions $g_{ij}(t)$.

eess.SY↗