arXiv subjects

Amir Leshem

Publications and source records attributed to Amir Leshem.

At least 37 records · Page 2Linked to original sources

arXiv2022

Communication Efficient Distributed Learning over Wireless Channels

Vertical distributed learning exploits the local features collected by multiple learning workers to form a better global model. However, the exchange of data between the workers and the model aggregator for parameter training incurs a heavy communication burden, especially when the learning system is built upon capacity-constrained wireless networks. In this paper, we propose a novel hierarchical distributed learning framework, where each worker separately learns a low-dimensional embedding of their local observed data. Then, they perform communication efficient distributed max-pooling for efficiently transmitting the synthesized input to the aggregator. For data exchange over a shared wireless channel, we propose an opportunistic carrier sensing-based protocol to implement the max-pooling operation for the output data from all the learning workers. Our simulation experiments show that the proposed learning framework is able to achieve almost the same model accuracy as the learning model using the concatenation of all the raw outputs from the learning workers, while requiring a communication load that is independent of the number of workers.

cs.NI↗

arXiv2022

Noisy Beeping Networks

We introduce noisy beeping networks, where nodes have limited communication capabilities, namely, they can only emit energy or sense the channel for energy. Furthermore, imperfections may cause devices to malfunction with some fixed probability when sensing the channel, which amounts to deducing a noisy received transmission. Such noisy networks have implications for ultra-lightweight sensor networks and biological systems. We show how to compute tasks in a noise-resilient manner over noisy beeping networks of arbitrary structure. In particular, we transform any algorithm that assumes a noiseless beeping network (of size $n$) into a noise-resilient version while incurring a multiplicative overhead of only $O(\log n)$ in its round complexity, with high probability. We show that our coding is optimal for some tasks, such as node-coloring of a clique. We further show how to simulate a large family of algorithms designed for distributed networks in the CONGEST($B$) model over a noisy beeping network. The simulation succeeds with high probability and incurs an asymptotic multiplicative overhead of $O(B\cdot Δ\cdot \min(n,Δ^2))$ in the round complexity, where $Δ$ is the maximal degree of the network. The overhead is tight for certain graphs, e.g., a clique. Further, this simulation implies a constant overhead coding for constant-degree networks.

cs.DS↗

arXiv2022

Non-convex Generalized Nash Games for Energy Efficient Power Allocation and Beamforming in mmWave Networks

Network management is a fundamental ingredient for efficient operation of wireless networks. With increasing bandwidth, number of antennas and number of users, the amount of information required for network management increases significantly. Therefore, distributed network management is a key to efficient operation of future networks. This paper focuses on the problem of distributed joint beamforming control and power allocation in ad-hoc mmWave networks. Over the shared spectrum, a number of multi-input-multi-output links attempt to minimize their supply power by simultaneously finding the locally optimal power allocation and beamformers in a self-organized manner. Our design considers a family of non-convex quality-of-service constraint and utility functions characterized by monotonicity in the strategies of the various users. We propose a two-stage, decentralized optimization scheme, where the adaptation of power levels and beamformer coefficients are iteratively performed by each link. We first prove that given a set of receive beamformers, the power allocation stage converges to an optimal generalized Nash equilibrium of the generalized power allocation game. Then we prove that iterative minimum-mean-square-error adaptation of the receive beamformer results in an overall converging scheme. Several transmit beamforming schemes requiring different levels of information exchange are also compared in the proposed allocation framework. Our simulation results show that allowing each link to optimize its transmit filters using the direct channel results in a near optimum performance with very low computational complexity, even though the problem is highly non-convex.

cs.NI↗

arXiv2021

Decentralized Learning for Channel Allocation in IoT Networks over Unlicensed Bandwidth as a Contextual Multi-player Multi-armed Bandit Game

We study a decentralized channel allocation problem in an ad-hoc Internet of Things network underlaying on the spectrum licensed to a primary cellular network. In the considered network, the impoverished channel sensing/probing capability and computational resource on the IoT devices make them difficult to acquire the detailed Channel State Information (CSI) for the shared multiple channels. In practice, the unknown patterns of the primary users' transmission activities and the time-varying CSI (e.g., due to small-scale fading or device mobility) also cause stochastic changes in the channel quality. Decentralized IoT links are thus expected to learn channel conditions online based on partial observations, while acquiring no information about the channels that they are not operating on. They also have to reach an efficient, collision-free solution of channel allocation with limited coordination. Our study maps this problem into a contextual multi-player, multi-armed bandit game, and proposes a purely decentralized, three-stage policy learning algorithm through trial-and-error. Theoretical analyses shows that the proposed scheme guarantees the IoT links to jointly converge to the social optimal channel allocation with a sub-linear (i.e., polylogarithmic) regret with respect to the operational time. Simulations demonstrate that it strikes a good balance between efficiency and network scalability when compared with the other state-of-the-art decentralized bandit algorithms.

cs.MA↗

arXiv2021

Distributed learning in congested environments with partial information

How can non-communicating agents learn to share congested resources efficiently? This is a challenging task when the agents can access the same resource simultaneously (in contrast to multi-agent multi-armed bandit problems) and the resource valuations differ among agents. We present a fully distributed algorithm for learning to share in congested environments and prove that the agents' regret with respect to the optimal allocation is poly-logarithmic in the time horizon. Performance in the non-asymptotic regime is illustrated in numerical simulations. The distributed algorithm has applications in cloud computing and spectrum sharing. Keywords: Distributed learning, congestion games, poly-logarithmic regret.

cs.MA↗

arXiv2021

Distributed Deep Reinforcement Learning for Collaborative Spectrum Sharing

Spectrum sharing among users is a fundamental problem in the management of any wireless network. In this paper, we discuss the problem of distributed spectrum collaboration without central management under general unknown channels. Since the cost of communication, coordination and control is rapidly increasing with the number of devices and the expanding bandwidth used there is an obvious need to develop distributed techniques for spectrum collaboration where no explicit signaling is used. In this paper, we combine game-theoretic insights with deep Q-learning to provide a novel asymptotically optimal solution to the spectrum collaboration problem. We propose a deterministic distributed deep reinforcement learning(D3RL) mechanism using a deep Q-network (DQN). It chooses the channels using the Q-values and the channel loads while limiting the options available to the user to a few channels with the highest Q-values and among those, it selects the least loaded channel. Using insights from both game theory and combinatorial optimization we show that this technique is asymptotically optimal for large overloaded networks. The selected channel and the outcome of the successful transmission are fed back into the learning of the deep Q-network to incorporate it into the learning of the Q-values. We also analyzed performance to understand the behavior of D3RL in differ

eess.SP↗

arXiv2021

Game of Thrones: Fully Distributed Learning for Multi-Player Bandits

We consider an N-player multi-armed bandit game where each player chooses one out of M arms for T turns. Each player has different expected rewards for the arms, and the instantaneous rewards are independent and identically distributed or Markovian. When two or more players choose the same arm, they all receive zero reward. Performance is measured using the expected sum of regrets, compared with an optimal assignment of arms to players that maximizes the sum of expected rewards. We assume that each player only knows her actions and the reward she received each turn. Players cannot observe the actions of other players, and no communication between players is possible. We present a distributed algorithm and prove that it achieves an expected sum of regrets of near-O\left(\log T\right). This is the first algorithm to achieve a near order optimal regret in this fully distributed scenario. All other works have assumed that either all players have the same vector of expected rewards or that communication between players is possible.

cs.GT↗

arXiv2021

The Restless Hidden Markov Bandit with Linear Rewards and Side Information

In this paper we present a model for the hidden Markovian bandit problem with linear rewards. As opposed to current work on Markovian bandits, we do not assume that the state is known to the decision maker before making the decision. Furthermore, we assume structural side information where the decision maker knows in advance that there are two types of hidden states; one is common to all arms and evolves according to a Markovian distribution, and the other is unique to each arm and is distributed according to an i.i.d. process that is unique to each arm. We present an algorithm and regret analysis to this problem. Surprisingly, we can recover the hidden states and maintain logarithmic regret in the case of a convex polytope action set. Furthermore, we show that the structural side information leads to expected regret that does not depend on the number of extreme points in the action space. Therefore, we obtain practical solutions even in high dimensional problems.

cs.LG↗

arXiv2020

Thermal instabilities, frequency comb formation, and temporal oscillations in Kerr microresonators

We analyze the consequences of dissipative heating in driven Kerr microresonators theoretically and numerically, using a thermal Lugiato-Lefever model. We show that thermal sensitivity modifies the stability range of continuous wave in a way that blocks direct access to broadband frequency-comb forming waveforms, and we propose a deterministic access path that bypasses the thermal instability barrier. We describe a novel thermal instability that leads to thermooptical oscillations via a Hopf bifurcation.

physics.optics↗

arXiv2020

My Fair Bandit: Distributed Learning of Max-Min Fairness with Multi-player Bandits

Consider N cooperative but non-communicating players where each plays one out of M arms for T turns. Players have different utilities for each arm, representable as an NxM matrix. These utilities are unknown to the players. In each turn players select an arm and receive a noisy observation of their utility for it. However, if any other players selected the same arm that turn, all colliding players will all receive zero utility due to the conflict. No other communication or coordination between the players is possible. Our goal is to design a distributed algorithm that learns the matching between players and arms that achieves max-min fairness while minimizing the regret. We present an algorithm and prove that it is regret optimal up to a $\log\log T$ factor. This is the first max-min fairness multi-player bandit algorithm with (near) order optimal regret.

cs.GT↗

arXiv2020

Multi-Gigabit Wireline Systems over Copper: An Interference Cancellation Perspective

Interference cancellation is the main driving technology in enhancing the transmission rates over telephone lines above 100 Mbps. Still, crosstalk interference in multi-pair digital subscriber line (DSL) systems at higher frequencies has not been dealt with sufficiently. The upcoming G.(mg) fast DSL system envisions the use of extremely high bandwidth and full-duplex transmissions generating significantly higher crosstalk and self-interference signals. More powerful interference cancellation techniques are required to enable multi-gigabit per second data rate transmission over copper lines. In this article, we analyze the performance of interference cancellation techniques, with a focus on novel research approaches and design considerations for efficient interference mitigation for multi-gigabit transmission over standard copper lines. We also detail novel approaches for interference cancellation in the upcoming technologies.

eess.SP↗

arXiv2019

The Interference Channel Revisited: Aligning Interference by Adjusting Receive Antenna Separation

It is shown that a receiver equipped with two antennas may null an arbitrary large number of spatial directions to any desired accuracy, while maintaining the interference-free signal-to-noise ratio, by judiciously adjusting the distance between the antenna elements. The main theoretical result builds on ergodic theory. The practicality of the scheme in moderate signal-to-noise systems is demonstrated for a scenario where each transmitter is equipped with a single antenna and each receiver has two receive chains and where the desired spacing between antenna elements is achieved by selecting the appropriate antennas from a large linear antenna array. We further extend the proposed scheme to show that interference can be eliminated also in specular multipath channels as well as multiple-input multiple-output interference channels where a single extra receiver suffices to align all interferers into a one-dimensional subspace. To demonstrate the performance of the scheme, we show significant gains for interference channels with four as well as six users, at low to moderate signal-to-noise ratios (0-20 dB). The robustness of the proposed technique to small channel estimation errors is also explored.

cs.IT↗

arXiv2019

Eliminating Interference in LOS Massive Multi-User MIMO with a Few Transceivers

Wireless cellular communication networks are bandwidth and interference limited. An important means to overcome these resource limitations is the use of multiple antennas. Base stations equipped with a very large (massive) number of antennas have been the focus of recent research. A bottleneck in such systems is the limited number of transmit/receive chains. In this work, a line-of-sight (LOS) channel model is considered. It is shown that for a given number of interferers, it suffices that the number of transmit/receive chains exceeds the number of desired users by one, assuming a sufficiently large antenna array. From a theoretical point of view, this is the first result proving the near-optimal performance of antenna selection, even when the total number of signals (desired and interfering) is larger than the number of receive chains. Specifically, a single additional chain suffices to reduce the interference to any desired level. We prove that using the proposed selection, a simple linear receiver/transmitter for the uplink/downlink provides near-optimal rates. In particular, in the downlink direction, there is no need for complicated dirty paper coding; each user can use an optimal code for a single user interference-free channel. In the uplink direction, there is almost no gain in implementing joint decoding. The proposed approach is also a significant improvement both from system and computational perspectives. Simulation results demonstrating the performance of the proposed method are provided.

eess.SP↗

arXiv2019

Distributed Learning for Channel Allocation Over a Shared Spectrum

Channel allocation is the task of assigning channels to users such that some objective (e.g., sum-rate) is maximized. In centralized networks such as cellular networks, this task is carried by the base station which gathers the channel state information (CSI) from the users and computes the optimal solution. In distributed networks such as ad-hoc and device-to-device (D2D) networks, no base station exists and conveying global CSI between users is costly or simply impractical. When the CSI is time varying and unknown to the users, the users face the challenge of both learning the channel statistics online and converge to a good channel allocation. This introduces a multi-armed bandit (MAB) scenario with multiple decision makers. If two users or more choose the same channel, a collision occurs and they all receive zero reward. We propose a distributed channel allocation algorithm that each user runs and converges to the optimal allocation while achieving an order optimal regret of O\left(\log T\right). The algorithm is based on a carrier sensing multiple access (CSMA) implementation of the distributed auction algorithm. It does not require any exchange of information between users. Users need only to observe a single channel at a time and sense if there is a transmission on that channel, without decoding the transmissions or identifying the transmitting users. We demonstrate the performance of our algorithm using simulated LTE and 5G channels.

cs.IT↗

arXiv2018

Approximate Best-Response Dynamics in Random Interference Games

In this paper we develop a novel approach to the convergence of Best-Response Dynamics for the family of interference games. Interference games represent the fundamental resource allocation conflict between users of the radio spectrum. In contrast to congestion games, interference games are generally not potential games. Therefore, proving the convergence of the best-response dynamics to a Nash equilibrium in these games requires new techniques. We suggest a model for random interference games, based on the long term fading governed by the players' geometry. Our goal is to prove convergence of the approximate best-response dynamics with high probability with respect to the randomized game. We embrace the asynchronous model in which the acting player is chosen at each stage at random. In our approximate best-response dynamics, the action of a deviating player is chosen at random among all the approximately best ones. We show that with high probability, with respect to the players' geometry and asymptotically with the number of players, each action increases the expected social-welfare (sum of achievable rates). Hence, the induced sum-rate process is a submartingale. Based on the Martingale Convergence Theorem, we prove convergence of the strategy profile to an approximate Nash equilibrium with good performance for asymptotically almost all interference games. We use the Markovity of the induced sum-rate process to provide probabilistic bounds on the convergence time. Finally, we demonstrate our results in simulated examples.

cs.GT↗

arXiv2018

Game Theoretic Dynamic Channel Allocation for Frequency-Selective Interference Channels

We consider the problem of distributed channel allocation in large networks under the frequency-selective interference channel. Performance is measured by the weighted sum of achievable rates. Our proposed algorithm is a modified Fictitious Play algorithm that can be implemented distributedly and its stable points are the pure Nash equilibria of a given game. Our goal is to design a utility function for a non-cooperative game such that all of its pure Nash equilibria have close to optimal global performance. This will make the algorithm close to optimal while requiring no communication between users. We propose a novel technique to analyze the Nash equilibria of a random interference game, determined by the random channel gains. Our analysis is asymptotic in the number of users. First we present a natural non-cooperative game where the utility of each user is his achievable rate. It is shown that, asymptotically in the number of users and for strong enough interference, this game exhibits many bad equilibria. Then we propose a novel non-cooperative M Frequency-Selective Interference Channel Game (M-FSIG), as a slight modification of the former, where the utility of each user is artificially limited. We prove that even its worst equilibrium has asymptotically optimal weighted sum-rate for any interference regime and even for correlated channels. This is based on an order statistics analysis of the fading channels that is valid for a broad class of fading distributions (including Rayleigh, Rician, m-Nakagami and more). We carry out simulations that show fast convergence of our algorithm to the proven asymptotically optimal pure Nash equilibria.

cs.IT↗

arXiv2018

Asymptotically Optimal Resource Block Allocation With Limited Feedback

Consider a channel allocation problem over a frequency-selective channel.There are K channels (frequency bands) and N users such that K=bN for some positive integer b. We want to allocate b channels (or resource blocks) to each user. Due to the nature of the frequency-selective channel, each user considers some channels to be better than others. The optimal solution to this resource allocation problem can be computed using the Hungarian algorithm. However, this requires knowledge of the numerical value of all the channel gains, which makes this approach impractical for large networks. We suggest a suboptimal approach, that only requires knowing what the M-best channels of each user are. We find the minimal value of M such that there exists an allocation where all the b channels each user gets are among his M-best. This leads to feedback of significantly less than one bit per user per channel. For a large class of fading distributions, including Rayleigh, Rician, m-Nakagami and others, this suboptimal approach leads to both an asymptotically (in K) optimal sum-rate and an asymptotically optimal minimal rate. Our non-opportunistic approach achieves (asymptotically) full multiuser diversity as well as optimal fairness, by contrast to all other limited feedback algorithms.

cs.IT↗

arXiv2018

Finite sample performance of linear least squares estimation

Linear Least Squares is a very well known technique for parameter estimation, which is used even when sub-optimal, because of its very low computational requirements and the fact that exact knowledge of the noise statistics is not required. Surprisingly, bounding the probability of large errors with finitely many samples has been left open, especially when dealing with correlated noise with unknown covariance. In this paper we analyze the finite sample performance of the linear least squares estimator. Using these bounds we obtain accurate bounds on the tail of the estimator's distribution. We show the fast exponential convergence of the number of samples required to ensure a given accuracy with high probability. We analyze a sub-Gaussian setting with a fixed or random design matrix of the linear least squares problem. We also extend the results to the case of a martingale difference noise sequence. Our analysis method is simple and uses simple $L_{\infty}$ type bounds on the estimation error. We also provide probabilistic finite sample bounds on the estimation error $L_2$ norm. The tightness of the bounds is tested through simulation. We demonstrate that our results are tighter than previously proposed bounds for $L_{\infty}$ norm of the error. The proposed bounds make it possible to predict the number of samples required for least squares estimation even when the least squares is sub-optimal and is used for computational simplicity.

math.ST↗