Due to the non-smoothness of optimization problems in Machine Learning, generalized smoothness assumptions have been gaining a lot of attention in recent years. One of the most popular assumptions of this type is $(L_0,L_1)$-smoothness (Zhang et al., 2020). In this paper, we focus on the class of (strongly) convex $(L_0,L_1)$-smooth functions and derive new convergence guarantees for several existing methods. In particular, we derive improved convergence rates for Gradient Descent with (Smoothed) Gradient Clipping and for Gradient Descent with Polyak Stepsizes. In contrast to the existing results, our rates do not rely on the standard smoothness assumption and do not suffer from the exponential dependency on the initial distance to the solution. We also extend these results to the stochastic case under the over-parameterization assumption, propose a new accelerated method for convex $(L_0,L_1)$-smooth optimization, and derive new convergence rates for Adaptive Gradient Descent (Malitsky and Mishchenko, 2020).

Introduced by Korpelevich in 1976, the extragradient method (EG) has become a cornerstone technique for solving min-max optimization, root-finding problems, and variational inequalities (VIs). Despite its longstanding presence and significant attention within the optimization community, most works focusing on understanding its convergence guarantees assume the strong $L$-Lipschitz condition. In this work, building on the proposed assumptions by Zhang et al. [2019] for minimization and Vankov et al. [2024a] for VIs, we focus on the more relaxed $\alpha$-symmetric $(L_0, L_1)$-Lipschitz condition. This condition generalizes the standard Lipschitz assumption by allowing the Lipschitz constant to scale with the operator norm, providing a more refined characterization of problem structures in modern machine learning. Under the $\alpha$-symmetric $(L_0, L_1)$-Lipschitz condition, we propose a novel step size strategy for EG to solve root-finding problems and establish sublinear convergence rates for monotone operators and linear convergence rates for strongly monotone operators. Additionally, we prove local convergence guarantees for weak Minty operators. We supplement our analysis with experiments validating our theory and demonstrating the effectiveness and robustness of the proposed step sizes for EG.

Traditional Federated Learning (FL) approaches assume collaborative clients with aligned objectives working towards a shared global model. However, in many real-world scenarios, clients act as rational players with individual objectives and strategic behaviors, a concept that existing FL frameworks are not equipped to adequately address. To bridge this gap, we introduce *Multiplayer Federated Learning (MpFL)*, a novel framework that models the clients in the FL environment as players in a game-theoretic context, aiming to reach an equilibrium. In this scenario, each player tries to optimize their own utility function, which may not align with the collective goal. Within MpFL, we propose *Per-Player Local Stochastic Gradient Descent (PEARL-SGD)*, an algorithm in which each player/client performs local updates independently and periodically communicates with other players. We theoretically analyze PEARL-SGD and prove that it reaches a neighborhood of equilibrium with less communication in the stochastic setup compared to its non-local counterpart. Finally, we verify our theoretical findings through numerical experiments.

Distributed and federated learning algorithms and techniques associated primarily with minimization problems. However, with the increase of minimax optimization and variational inequality problems in machine learning, the necessity of designing efficient distributed/federated learning approaches for these problems is becoming more apparent. In this paper, we provide a unified convergence analysis of communication-efficient local training methods for distributed variational inequality problems (VIPs). Our approach is based on a general key assumption on the stochastic estimates that allows us to propose and analyze several novel local training algorithms under a single framework for solving a class of structured non-monotone VIPs. We present the first local gradient descent-accent algorithms with provable improved communication complexity for solving distributed variational inequalities on heterogeneous data. The general algorithmic framework recovers state-of-the-art algorithms and their sharp convergence guarantees when the setting is specialized to minimization or minimax optimization problems. Finally, we demonstrate the strong performance of the proposed algorithms compared to state-of-the-art methods when solving federated minimax optimization problems.

Adaptive methods are extremely popular in machine learning as they make learning rate tuning less expensive. This paper introduces a novel optimization algorithm named KATE, which presents a scale-invariant adaptation of the well-known AdaGrad algorithm. We prove the scale-invariance of KATE for the case of Generalized Linear Models. Moreover, for general smooth non-convex problems, we establish a convergence rate of $O((\log T)/\sqrt{T})$ for KATE, matching the best-known ones for AdaGrad and Adam. We also compare KATE to other state-of-the-art adaptive algorithms Adam and AdaGrad in numerical experiments with different problems, including complex machine learning tasks like image classification and text classification on real data. The results indicate that KATE consistently outperforms AdaGrad and matches/surpasses the performance of Adam in all considered scenarios.

Single-call stochastic extragradient methods, like stochastic past extragradient (SPEG) and stochastic optimistic gradient (SOG), have gained a lot of interest in recent years and are one of the most efficient algorithms for solving large-scale min-max optimization and variational inequalities problems (VIP) appearing in various machine learning tasks. However, despite their undoubted popularity, current convergence analyses of SPEG and SOG require strong assumptions like bounded variance or growth conditions. In addition, several important questions regarding the convergence properties of these methods are still open, including mini-batching, efficient step-size selection, and convergence guarantees under different sampling strategies. In this work, we address these questions and provide convergence guarantees for two large classes of structured non-monotone VIPs: (i) quasi-strongly monotone problems (a generalization of strongly monotone problems) and (ii) weak Minty variational inequalities (a generalization of monotone and Minty VIPs). We introduce the expected residual condition, explain its benefits, and show how it allows us to obtain a strictly weaker bound than previously used growth conditions, expected co-coercivity, or bounded variance assumptions. Finally, our convergence analysis holds under the arbitrary sampling paradigm, which includes importance sampling and various mini-batching strategies as special cases.

In order to meet the exponential increase in wireless demand, new technologies are being considered for next-generation Wi-Fi systems (e.g., IEEE 802.11ax). Among these technologies is the adaptation of clear channel assessment (CCA) thresholds for high-efficiency (HE) stations (STAs) according to the beacon's received signal strength indicator (RSSI). The motivation behind this approach is to enhance the network throughput by improving the spatial reuse (i.e., allowing simultaneous transmissions from nearby STAs). There exists an inherent tradeoff between increasing the network throughput, via adapting the CCA thresholds for HE STAs, and maintaining fairness between legacy and HE STAs. In this paper, we provide a theoretical framework to evaluate the aforementioned tradeoff. We also propose a centralized fairness mechanism (CFM), in which STAs switch between an adaptive phase (CCA adaptation is allowed) and a fixed phase (legacy and HE STAs use the same CCA threshold). We formulate an optimization problem with the objective of determining the optimal switching strategy that maximizes the network throughput while maintaining a lower bound on per-STA throughput. Finally, we validate the proposed mechanism using simulations.

In this paper, we study the baseband estimation of the frequency- dependent imbalance between the in-phase and quadrature branches (I/Q imbalance) of a direct-conversion receiver, by exploiting the preambles which is not specially designed for I/Q imbalance estimation. We propose an in-service estimation method which consists of two stages: the first stage utilizes the existing preambles in a standard-compliant system to estimate the frequency-independent component of the I/Q imbalances on only a subset of subcarriers; in the second stage, a blind estimation method is proposed to estimate the frequency-dependent component of I/Q imbalances on all subcarriers, based on the result of the first stage and the second-order statistics of the received signal. The proposed estimation method is applicable to commonly used multi-carrier systems.

The default medium access mechanism for Wi-Fi, Distributed Coordination Function (DCF), is a simple contention based protocol aimed at providing a fair distribution of resources among Wi-Fi nodes. However, DCF suffers from significant performance degradation in the presence of dense deployments. Hence, improving the performance of the Wi-Fi MAC layer is essential for efficient spectrum sharing among overlapping Basic Subscriber Set (OBSS) for next generation wireless networks. In this context, in this paper, we compare DCF with an existing Wi-Fi mechanisms, Power-Save Multi-Poll (PSMP) and Hybrid Coordination Function (HCF) Controlled Channel Access (HCCA), and show that, although standard scheduled access techniques enhance WiFi throughput, they also suffer a decrease on performance in dense deployments. As a starting point, we propose that scheduled access including contention-free channel access mechanisms should be considered in addition to DCF for dense deployments.

The increasing commercial success of Wi-Fi and the wireless communication industry forecast of exponential traffic growth for the next years indicate Wi-Fi dense deployments as scenarios more and more common in the future. Wi-Fi was not designed to operate in such scenarios. Because of its contention based channel access and backoff procedure, Wi-Fi presents low channel access efficiency and sensible performance degradation in terms of user throughput for dense deployments. This paper discusses the challenges of Wi-Fi operation in dense deployment scenarios and the benefits of a proposed adaptive transmit power mechanism. Wi-Fi performance is assessed by standard compliant simulations.

This paper presents the design of multiple-input multiple-output (MIMO) coordinated beamforming (CBF) techniques that greatly decrease packet decoding failure due to collisions at co-channel 802.11 WLAN access points (APs). Specifically, we advocate a new WLAN paradigm that promotes the sharing of channel state information (CSI) and uplink precoders between co-channel APs that are capable of multipacket reception (MPR). PHY-layer MIMO CBF design algorithms based on joint and sequential computation that satisfy network-wide MPR conditions are presented. Numerical examples illustrate that the proposed CBF schemes greatly outperform uncoordinated methods in terms of successful packet detection.

The recent development of regulatory policies that permit the use of TV bands spectrum on a secondary basis has motivated discussion about coexistence of primary (e.g. TV broadcasts) and secondary users (e.g. WiFi users in TV spectrum). However, much less attention has been given to coexistence of different secondary wireless technologies in the TV white spaces. Lack of coordination between secondary networks may create severe interference situations, resulting in less efficient usage of the spectrum. In this paper, we consider two of the most prominent wireless technologies available today, namely Long Term Evolution (LTE), and WiFi, and address some problems that arise from their coexistence in the same band. We perform exhaustive system simulations and observe that WiFi is hampered much more significantly than LTE in coexistence scenarios. A simple coexistence scheme that reuses the concept of almost blank subframes in LTE is proposed, and it is observed that it can improve the WiFi throughput per user up to 50 times in the studied scenarios.

The deployment of modern mobile systems has faced severe challenges due to the current spectrum scarcity. The situation has been further worsened by the development of different wireless technologies and standards that can be used in the same frequency band. Furthermore, the usage of smaller cells (e.g. pico, femto and wireless LAN), coexistence among heterogeneous networks (including amongst different wireless technologies such as LTE and Wi-Fi deployed in the same frequency band) has been a big field of research in the academy and industry. In this paper, we provide a performance evaluation of coexistence between LTE and Wi-Fi systems and show some of the challenges faced by the different technologies. We focus on a simulator-based system- level analysis in order to assess the network performance in an office scenario. Simulation results show that LTE system performance is slightly affected by coexistence whereas Wi-Fi is significantly impacted by LTE transmissions. In coexistence, the Wi-Fi channel is most often blocked by LTE interference, making the Wi-Fi nodes to stay on the LISTEN mode more than 96% of the time. This reflects directly on the Wi-Fi user throughput, that decreases from 70% to ≈100% depending on the scenario. Finally, some of the main issues that limit the LTE/Wi-Fi coexistence and some pointers on the mutual interference management of both the systems are provided.

Spectrum sharing is a powerful alternative to deal with the exponential increase on the wireless communication capacity demand. In this context, the coexistence of two of the most prominent wireless technologies today, Long Term Evolution (LTE) and Wi-Fi, is an important research topic. In the most common Wi-Fi network operation, the Distributed Coordination Function (DCF), communication nodes access the channel only if the interference level is below a certain threshold. Then, Wi-Fi operation is severely affected when in coexistence with LTE. This paper proposes the use of LTE uplink (UL) power control to improve LTE/Wi-Fi coexistence. With the introduction of an additional factor to the conventional LTE UL power control, a controlled decrease of LTE UL transmit powers is carried out according to interference measurements, giving opportunity to Wi-Fi transmissions. The proposed LTE UL power control with interference aware power operating point is a flexible tool to deal with the trade-off between LTE and Wi-Fi performances in coexistence, since it is able to set different LTE/Wi-Fi coexistence configurations with the choice of a single parameter. Simulation results show that the proposed approach can provide similar or better performance for both LTE and Wi-Fi networks than a previously proposed interference avoidance mechanism.

Collecting sensory data at access point (AP) from large number of sensor nodes with low latency is a critical issue. In Wi-Fi, prior to uplink data delivery, AP typically needs to poll large number of sensor nodes sequentially and allocate channel resources to individual node resulting in large latency. An efficient method to reduce the latency and power consumption in wireless sensor networks is to parallelize the polling operation so that multiple nodes can concurrently respond to the poll request of an AP by sending orthogonal sequences with uplink power control. In this paper, we present a conceptually simple uplink power control scheme for the parallel polling operation between AP and low power sensor nodes. We formulate the uplink power control problem as a sequence design problem and show that uplink channel state information (CSI) required to achieve a given target receive SNR can be significantly reduced by carefully designing sequences. We further develop a low complexity instantaneous (fast) power control scheme in order to reduce the number of computations required by the low power sensor node. We also analyze and compare the detection performance of the instantaneous (fast) and average (slow) power control schemes in terms of diversity gain.

A major challenge in low power sensor networks is collecting data from large number of nodes with low latency. Access point (AP) typically needs to poll large number of nodes individually and schedule transmission times for each of the nodes resulting in large latency. In this paper, we propose a physical layer technique that parallelizes the polling response from multiple nodes (so called parallel acknowledgment) in order to decrease the latency. Each node responds to the poll request of an AP by using the well-known Zadoff-Chu (ZC) sequences. By using the orthogonal properties of the ZC sequences, the AP is able to resolve the multiple signatures of different nodes simultaneously. We further develop low complexity transmission scheme for the ZC sequences in order to reduce the number of computations and complexity required by the low power sensor nodes. We also compare the performance of both time and frequency domain receivers.

This paper addresses the problem of frequency domain packet scheduling (FDPS) incorporating spatial division multiplexing (SDM) multiple input multiple output (MIMO) techniques on the 3GPP Long-Term Evolution (LTE) downlink. We impose the LTE MIMO constraint of selecting only one MIMO mode (spatial multiplexing or transmit diversity) per user per transmission time interval (TTI). First, we address the optimal MIMO mode selection (multiplexing or diversity) per user in each TTI in order to maximize the proportional fair (PF) criterion adapted to the additional frequency and spatial domains. We prove that both single-user (SU-) and multi-user (MU-) MIMO FDPS problems under the LTE requirement are NP-hard. We therefore develop two types of approximation algorithms (ones with full channel feedback and the others with partial channel feedback), all of which guarantee provable performance bounds for both SU- and MU-MIMO cases. Based on 3GPP LTE system model simulations, our approximation algorithms that take into account both spatial and frequency diversity gains outperform the exact algorithms that do not exploit the potential spatial diversity gain. Moreover, the approximation algorithms with partial channel feedback achieve comparable performance (with only 1-6 percent performance degradation) to the ones with full channel feedback, while significantly reducing the channel feedback overhead by nearly 50 percent.

This paper addresses the problem of frequency domain packet scheduling (FDPS) incorporating spatial division multiplexing (SDM) multiple input multiple output (MIMO) techniques on the 3GPP long term evolution (LTE) downlink. We impose the LTE MIMO constraint of selecting only one MIMO mode (spatial multiplexing or transmit diversity) per user per transmission time interval (TTI). First, we address the optimal MIMO mode selection (multiplexing or diversity) per user in each TTI in order to maximize the proportional fair (PF) criterion extended to frequency and spatial domains. We prove that the SU-MIMO (single-user MIMO) FDPS problem under the LTE requirement is NP-hard and therefore, we develop two approximation algorithms (one with full channel feedback and the other with partial channel feedback) with provable performance bounds. Based on 3GPP LTE system model simulations, the approximation algorithm with partial channel feedback is shown to have comparable performance to the one with full channel feedback, while significantly reducing the channel feedback overhead by nearly 50%.

As wireless local area networks (WLANs) become a part of our network infrastructure, it is critical that we understand both the performance provided to the end users and the capacity of these WLANs in terms of the number of supported flows (calls). Since it is clear that video traffic, as well as voice and data, will be carried by these networks, it is particularly important that we investigate these issues for packetized video. In this paper, we investigate the video user capacity of wireless networks subject to a multiuser perceptual quality constraint. As a particular example, we study the transmission of AVC/H.264 coded video streams over an IEEE 802.11a WLAN subject to a constraint on the quality of the delivered video experienced by r% (75%, for example) of the users of the WLAN. This work appears to be the first such effort to address this difficult but important problem. Furthermore, the methodology employed is perfectly general and can be used for different networks, video codecs, transmission channels, protocols, and perceptual quality measures.

We consider the lossy transmission of source information over Rayleigh fading channels. We investigate the utility of two channel capacity definitions, ergodic capacity, where it is assumed that the channel cycles through all fading states, and outage capacity, where the source is transmitted at a constant rate with a specified outage probability. We also study the outage rate and expected source distortion for different outage probabilities. It is observed that the outage probabilities required to maximize outage rate and minimize expected distortion are quite different. This implies that schemes based on maximizing capacity might not lead to the most efficient design for lossy transmission of source information over wireless networks. We show that minimizing expected distortion over a wireless link does not necessarily minimize the variance of the distortion, and hence parameter selection based on minimizing expected distortion can lead to a high distortion for a specific realization. We also introduce different performance measures that take into account the variance of source distortion and might be more suitable for source transmission over fading channels. Finally, we observe that in a Rayleigh fading channel in the presence of channel state information (CSI) at both the transmitter and receiver, in addition to a capacity distribution, there is a source distortion distribution at the receiver for a memoryless Gaussian source. A careful investigation of the capacity and source distortion distributions reveal that the probability of achieving the average source distortion increases with an increase in average signal to noise ratio (SNR) while the probability of achieving the average capacity does not change significantly with SNR.

Emerging as the method of choice for compressing video over WLANs, the AVC/H.264 standard is a suite of coding options and parameters whose values are to be chosen for specific videos and channel conditions. We investigate the tradeoffs in performance across the quantization parameter (QP), the group of picture size (GOPS), the payload size (PS), physical layer (PHY) data rate in 802.11a, and the average channel SNR for multipath fading channels. The interesting and sometimes surprising results are: the delivered video quality is very sensitive to the change in PSs and in many cases the PS optimizing PHY throughput cannot yield acceptable video quality; although lower QP yields better video quality when there is no packet loss, when the quality is corrupted heavily due to packet losses, there is no advantage gained for finer quantization and higher bit rate; lower GOPS, i.e., to refresh I-frames more frequently does not necessarily improve the delivered video quality and in many cases medium values of GOPS should be chosen; different types of videos have dramatically different delivered quality in the same channel which should be taken into account in network evaluation and design.

The fundamental tradeoff in a WLAN with multiple video users is between the number of video users the WLAN can support and the perceptual quality each user experiences. Our previous work has investigated the delivered AVC/H.264 video quality over 802.11a WLANs with multipath fading. In this paper we study two extreme scenarios to formulate the upper and lower boundaries for video user capacity of an 802.11a WLAN operated under the contention based distributed coordination function (DCF): the worst scenario is when all users happen to be sending/receiving their intra-coded (I) frames at the same time and the best scenario is when all users happen to be coordinated in I frame refreshing. To calculate the video user capacity boundaries we study the dependence of coded video data rate on the properties of individual videos as well as the major video coding parameters: group of picture size (GOPS), quantization (QP) and video packet payload size (PS). Two heuristic formulas are proposed to calculate approximately the I frame and inter-coded (P) frame sizes respectively. The video user capacity boundaries are further explored in the context of the delivered video quality constraints investigated in our previous work.

We provide a theoretical framework for cross-layer design in multimedia communications to optimize single-user throughput by selecting the transmitted bit rate and payload size as a function of channel conditions for both additive white Gaussian noise (AWGN) and Nakagami-m fading channels. Numerical results reveal that careful payload length adaptation significantly improves the throughput performance at low signal to noise ratios (SNRs), while at higher SNRs, rate adaptation with higher payload lengths provides better throughput performance. Since we are interested in multimedia applications, we do not allow retransmissions in order to minimize latency and to reduce congestion on the wireless link and we assume that packet loss concealment will be used to compensate for lost packets. We also investigate the throughput and packet error rate performance over multipath frequency selective fading channels for typical payload sizes used in voice and video applications. We explore the difference in link adaptation thresholds for these payload sizes using the Nafteli Chayat multipath fading channel model, and we present a link adaptation scheme to maximize the throughput subject to a packet error rate constraint.

Multimedia transmission over wireless local area networks is challenging due to the varying nature of the wireless channel as well as the inherent difference between multimedia and data traffic. In the MAC layer, a single bit error in the packet can lead to the entire packet being discarded. This results in a higher packet error rate for larger payload sizes. Retransmission due to packet errors causes the contention window to double, and this leads to a decrease in throughput if the wireless channel does not improve for the retransmitted packets. Hence, throughput is a function of packet payload length as well as the maximum number of allowable retransmissions. In this paper, we investigate the effect of payload length adaptation and retransmissions on the throughput and capacity of multimedia users. Numerical results and simulations reveal that careful payload adaptation significantly improves the throughput performance at low signal to noise ratios (SNRs). It is also observed that excessive retransmissions reduce the effective throughput, thereby decreasing the capacity of multimedia users in the presence of data users. Since multimedia traffic is more latency constrained and less error constrained, by carefully selecting the payload length and maximum number of allowable retransmissions based on the channel conditions, a greater number of multimedia users can be supported.

The communication of voice over wireless local area networks (WLANs) is influenced by the choice of speech codec, packetization interval and PHY layer bit rates. These choices affect the number of voice users that can be supported on the WLAN as well as the speech quality experienced by each user. We investigate the effect of different combinations of these parameters for a 802.11a WLAN in different channel conditions with the objective of maximizing the number of voice users supported on the WLAN subject to a quality constraint. We use an indicator for assessing the speech quality experienced by a single user in a WLAN, based on a Perceptual Evaluation of Speech Quality (PESQ) Mean Opinion Score (MOS) constraint and the probability of a voice user achieving this constraint. The contributions of this paper are three-fold. First, a PHY layer rate adaptation scheme is proposed, in which the operating rate for each Signal to Noise Ratio (SNR) is chosen as the one that maximizes the capacity given a quality constraint. Second, based on the PHY layer rate adaptation scheme, we evaluate the effect of the choice of codec and voice payload size on the capacity values obtainable at different SNRs. Finally, we show the effect of channel conditions and the tightening of quality constraints on the capacity values at different SNRs.

Wireless local area networks offer a range of transmitted data rates that are to be selected according to estimated channel conditions. However, due to packet overheads and contention times introduced by the CSMA/CA multiple access protocol, effective throughput is much less than the transmitted bit rates. Furthermore, if there is even a single bit error in the packet, the entire packet is discarded and the packet is retransmitted. This causes the effective throughput to be a function of the packet payload length. We provide a theoretical framework to optimize single-user throughput by selecting the transmitted bit rate and payload size as a function of channel conditions for both additive white Gaussian noise (AWGN) and Nakagami-m fading channels. Numerical results reveal that careful payload adaptation significantly improves the throughput performance at low signal to noise ratios (SNRs) while at higher SNRs, rate adaptation with higher payload lengths provides better performance. We compare the range of SNRs over which payload length adaptation is crucial for AWGN and different fading channels based on the m-parameter of Nakagami fading realization. We then specify SNR values for switching between transmitted bit rates and payload lengths such that the effective throughput is maximized.

Wireless local area networks offer a range of transmitted data rates that are to be selected according to estimated channel conditions. However, due to packet overheads and contention times introduced by the CSMA/CA multiple access protocol, effective throughput is much less than the nominal data rates. Most multimedia applications use small payload sizes in order to ensure reliable, low latency transmission. This results in a further loss in effective throughput thereby reducing network capacity drastically. Thus, a cross-layer based design approach along with link adaptation is required to improve the network performance under different channel conditions. We investigate the effect of payload size variations on single-user throughput for both non-fading and multipath fading environments. We explore the difference in link adaptation thresholds for different payload sizes with varying channel characteristics. A link adaptation scheme to maximize the throughput with a packet error constraint is presented