Distributed Submodular Maximization with Limited Information

We consider a class of distributed submodular maximization problems in which each agent must choose a single strategy from its strategy set. The global objective is to maximize a submodular function of the strategies chosen by each agent. When choosing a strategy, each agent has access to only a limited number of other agents' choices. For each of its strategies, an agent can evaluate its marginal contribution to the global objective given its information. The main objective is to investigate how this limitation of information about the strategies chosen by other agents affects the performance when agents make choices according to a local greedy algorithm. In particular, we provide lower bounds on the performance of greedy algorithms for submodular maximization, which depend on the clique number of a graph that captures the information structure. We also characterize graph-theoretic upper bounds in terms of the chromatic number of the graph. Finally, we demonstrate how certain graph properties limit the performance of the greedy algorithm. Simulations on several common models for random networks demonstrate our results.Comment: 11 pages, 8 figure

Optimizing Beams and Bits: A Novel Approach for Massive MIMO Base-Station Design

We consider the problem of jointly optimizing ADC bit resolution and analog beamforming over a frequency-selective massive MIMO uplink. We build upon a popular model to incorporate the impact of low bit resolution ADCs, that hitherto has mostly been employed over flat-fading systems. We adopt weighted sum rate (WSR) as our objective and show that WSR maximization under finite buffer limits and important practical constraints on choices of beams and ADC bit resolutions can equivalently be posed as constrained submodular set function maximization. This enables us to design a constant-factor approximation algorithm. Upon incorporating further enhancements we obtain an efficient algorithm that significantly outperforms state-of-the-art ones.Comment: Tech. Report. Appeared in part in IEEE ICNC 2019. Added few more comments and corrected minor typo

Optimal Algorithms for Submodular Maximization with Distributed Constraints

We consider a class of discrete optimization problems that aim to maximize a submodular objective function subject to a distributed partition matroid constraint. More precisely, we consider a networked scenario in which multiple agents choose actions from local strategy sets with the goal of maximizing a submodular objective function defined over the set of all possible actions. Given this distributed setting, we develop Constraint-Distributed Continuous Greedy (CDCG), a message passing algorithm that converges to the tight $(1-1/e)$ approximation factor of the optimum global solution using only local computation and communication. It is known that a sequential greedy algorithm can only achieve a $1/2$ multiplicative approximation of the optimal solution for this class of problems in the distributed setting. Our framework relies on lifting the discrete problem to a continuous domain and developing a consensus algorithm that achieves the tight $(1-1/e)$ approximation guarantee of the global discrete solution once a proper rounding scheme is applied. We also offer empirical results from a multi-agent area coverage problem to show that the proposed method significantly outperforms the state-of-the-art sequential greedy method

Resilient Monotone Sequential Maximization

Applications in machine learning, optimization, and control require the sequential selection of a few system elements, such as sensors, data, or actuators, to optimize the system performance across multiple time steps. However, in failure-prone and adversarial environments, sensors get attacked, data get deleted, and actuators fail. Thence, traditional sequential design paradigms become insufficient and, in contrast, resilient sequential designs that adapt against system-wide attacks, deletions, or failures become important. In general, resilient sequential design problems are computationally hard. Also, even though they often involve objective functions that are monotone and (possibly) submodular, no scalable approximation algorithms are known for their solution. In this paper, we provide the first scalable algorithm, that achieves the following characteristics: system-wide resiliency, i.e., the algorithm is valid for any number of denial-of-service attacks, deletions, or failures; adaptiveness, i.e., at each time step, the algorithm selects system elements based on the history of inflicted attacks, deletions, or failures; and provable approximation performance, i.e., the algorithm guarantees for monotone objective functions a solution close to the optimal. We quantify the algorithm's approximation performance using a notion of curvature for monotone (not necessarily submodular) set functions. Finally, we support our theoretical analyses with simulated experiments, by considering a control-aware sensor scheduling scenario, namely, sensing-constrained robot navigation.Comment: correction of typo

An approximation algorithm for joint caching and recommendations in cache networks

Streaming platforms, like Netflix and YouTube, strive to offer a high quality of service (QoS) to their users. Meanwhile, a significant share of content consumption of these platforms is heavily influenced by recommendations. In this setting, user experience is a product of both the quality of the recommendations (QoR) and the quality of service (QoS) of the delivered content. However, network decisions (like caching) that affect QoS are usually made without taking into account the recommender's actions. Likewise, recommendation decisions are made independently of the potential delivery quality of the recommended content. The aim of this paper is to jointly optimize caching and recommendations in a generic network of caches, with the objective of maximizing the quality of experience (QoE). This is in line with the recent trend for large content providers to simultaneously act as Content Delivery Network (CDN) owners. We formulate this joint optimization problem and prove that it can be approximated up to a constant. We believe this to be the first polynomial algorithm to achieve a constant approximation ratio for the joint problem. Moreover, our numerical experiments show important performance gains of our algorithm over baseline schemes and existing algorithms in the literature