We study decentralized multi-agent learning in bipartite queueing systems, a standard model for service systems. In particular, N agents request service from K servers in a fully decentralized way, i.e, by running the same algorithm without communication. Previous decentralized algorithms are restricted to symmetric systems, have performance that is degrading exponentially in the number of servers, require communication through shared randomness and unique agent identities, and are computationally demanding. In contrast, we provide a simple learning algorithm that, when run decentrally by each agent, leads the queueing system to have efficient performance in general asymmetric bipartite queueing systems while also having additional robustness properties. Along the way, we provide the first provably efficient UCB-based algorithm for the centralized case of the problem.
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In this paper, we study the following nonlinear matrix decomposition (NMD) problem: given a sparse nonnegative matrix $X$, find a low-rank matrix $\Theta$ such that $X \approx f(\Theta)$, where $f$ is an element-wise nonlinear function. We focus on the case where $f(\cdot) = \max(0, \cdot)$, the rectified unit (ReLU) non-linear activation. We refer to the corresponding problem as ReLU-NMD. We first provide a brief overview of the existing approaches that were developed to tackle ReLU-NMD. Then we introduce two new algorithms: (1) aggressive accelerated NMD (A-NMD) which uses an adaptive Nesterov extrapolation to accelerate an existing algorithm, and (2) three-block NMD (3B-NMD) which parametrizes $\Theta = WH$ and leads to a significant reduction in the computational cost. We also propose an effective initialization strategy based on the nuclear norm as a proxy for the rank function. We illustrate the effectiveness of the proposed algorithms (available on gitlab) on synthetic and real-world data sets.
This monograph takes a step towards promoting the study of efficiency in the era of neural information retrieval by offering a comprehensive survey of the literature on efficiency and effectiveness in ranking, and to a limited extent, retrieval. This monograph was inspired by the parallels that exist between the challenges in neural network-based ranking solutions and their predecessors, decision forest-based learning to rank models, as well as the connections between the solutions the literature to date has to offer. We believe that by understanding the fundamentals underpinning these algorithmic and data structure solutions for containing the contentious relationship between efficiency and effectiveness, one can better identify future directions and more efficiently determine the merits of ideas. We also present what we believe to be important research directions in the forefront of efficiency and effectiveness in retrieval and ranking.
This paper studies a class of multi-agent reinforcement learning (MARL) problems where the reward that an agent receives depends on the states of other agents, but the next state only depends on the agent's own current state and action. We name it REC-MARL standing for REward-Coupled Multi-Agent Reinforcement Learning. REC-MARL has a range of important applications such as real-time access control and distributed power control in wireless networks. This paper presents a distributed policy gradient algorithm for REC-MARL. The proposed algorithm is distributed in two aspects: (i) the learned policy is a distributed policy that maps a local state of an agent to its local action and (ii) the learning/training is distributed, during which each agent updates its policy based on its own and neighbors' information. The learned algorithm achieves a stationary policy and its iterative complexity bounds depend on the dimension of local states and actions. The experimental results of our algorithm for the real-time access control and power control in wireless networks show that our policy significantly outperforms the state-of-the-art algorithms and well-known benchmarks.
An experimental comparison of two or more optimization algorithms requires the same computational resources to be assigned to each algorithm. When a maximum runtime is set as the stopping criterion, all algorithms need to be executed in the same machine if they are to use the same resources. Unfortunately, the implementation code of the algorithms is not always available, which means that running the algorithms to be compared in the same machine is not always possible. And even if they are available, some optimization algorithms might be costly to run, such as training large neural-networks in the cloud. In this paper, we consider the following problem: how do we compare the performance of a new optimization algorithm B with a known algorithm A in the literature if we only have the results (the objective values) and the runtime in each instance of algorithm A? Particularly, we present a methodology that enables a statistical analysis of the performance of algorithms executed in different machines. The proposed methodology has two parts. Firstly, we propose a model that, given the runtime of an algorithm in a machine, estimates the runtime of the same algorithm in another machine. This model can be adjusted so that the probability of estimating a runtime longer than what it should be is arbitrarily low. Secondly, we introduce an adaptation of the one-sided sign test that uses a modified \textit{p}-value and takes into account that probability. Such adaptation avoids increasing the probability of type I error associated with executing algorithms A and B in different machines.
Reinforcement Learning (RL) algorithms are known to scale poorly to environments with many available actions, requiring numerous samples to learn an optimal policy. The traditional approach of considering the same fixed action space in every possible state implies that the agent must understand, while also learning to maximize its reward, to ignore irrelevant actions such as $\textit{inapplicable actions}$ (i.e. actions that have no effect on the environment when performed in a given state). Knowing this information can help reduce the sample complexity of RL algorithms by masking the inapplicable actions from the policy distribution to only explore actions relevant to finding an optimal policy. While this technique has been formalized for quite some time within the Automated Planning community with the concept of precondition in the STRIPS language, RL algorithms have never formally taken advantage of this information to prune the search space to explore. This is typically done in an ad-hoc manner with hand-crafted domain logic added to the RL algorithm. In this paper, we propose a more systematic approach to introduce this knowledge into the algorithm. We (i) standardize the way knowledge can be manually specified to the agent; and (ii) present a new framework to autonomously learn the partial action model encapsulating the precondition of an action jointly with the policy. We show experimentally that learning inapplicable actions greatly improves the sample efficiency of the algorithm by providing a reliable signal to mask out irrelevant actions. Moreover, we demonstrate that thanks to the transferability of the knowledge acquired, it can be reused in other tasks and domains to make the learning process more efficient.
Bilevel optimization is one of the fundamental problems in machine learning and optimization. Recent theoretical developments in bilevel optimization focus on finding the first-order stationary points for nonconvex-strongly-convex cases. In this paper, we analyze algorithms that can escape saddle points in nonconvex-strongly-convex bilevel optimization. Specifically, we show that the perturbed approximate implicit differentiation (AID) with a warm start strategy finds $\epsilon$-approximate local minimum of bilevel optimization in $\tilde{O}(\epsilon^{-2})$ iterations with high probability. Moreover, we propose an inexact NEgative-curvature-Originated-from-Noise Algorithm (iNEON), a pure first-order algorithm that can escape saddle point and find local minimum of stochastic bilevel optimization. As a by-product, we provide the first nonasymptotic analysis of perturbed multi-step gradient descent ascent (GDmax) algorithm that converges to local minimax point for minimax problems.
Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path in a large graph, neural networks allow learning from data to predict the most likely answer in more complex tasks such as image classification, which cannot be reduced to an exact algorithm. To get the best of both worlds, this thesis explores combining both concepts leading to more robust, better performing, more interpretable, more computationally efficient, and more data efficient architectures. The thesis formalizes the idea of algorithmic supervision, which allows a neural network to learn from or in conjunction with an algorithm. When integrating an algorithm into a neural architecture, it is important that the algorithm is differentiable such that the architecture can be trained end-to-end and gradients can be propagated back through the algorithm in a meaningful way. To make algorithms differentiable, this thesis proposes a general method for continuously relaxing algorithms by perturbing variables and approximating the expectation value in closed form, i.e., without sampling. In addition, this thesis proposes differentiable algorithms, such as differentiable sorting networks, differentiable renderers, and differentiable logic gate networks. Finally, this thesis presents alternative training strategies for learning with algorithms.
The rapid changes in the finance industry due to the increasing amount of data have revolutionized the techniques on data processing and data analysis and brought new theoretical and computational challenges. In contrast to classical stochastic control theory and other analytical approaches for solving financial decision-making problems that heavily reply on model assumptions, new developments from reinforcement learning (RL) are able to make full use of the large amount of financial data with fewer model assumptions and to improve decisions in complex financial environments. This survey paper aims to review the recent developments and use of RL approaches in finance. We give an introduction to Markov decision processes, which is the setting for many of the commonly used RL approaches. Various algorithms are then introduced with a focus on value and policy based methods that do not require any model assumptions. Connections are made with neural networks to extend the framework to encompass deep RL algorithms. Our survey concludes by discussing the application of these RL algorithms in a variety of decision-making problems in finance, including optimal execution, portfolio optimization, option pricing and hedging, market making, smart order routing, and robo-advising.
This paper aims to mitigate straggler effects in synchronous distributed learning for multi-agent reinforcement learning (MARL) problems. Stragglers arise frequently in a distributed learning system, due to the existence of various system disturbances such as slow-downs or failures of compute nodes and communication bottlenecks. To resolve this issue, we propose a coded distributed learning framework, which speeds up the training of MARL algorithms in the presence of stragglers, while maintaining the same accuracy as the centralized approach. As an illustration, a coded distributed version of the multi-agent deep deterministic policy gradient(MADDPG) algorithm is developed and evaluated. Different coding schemes, including maximum distance separable (MDS)code, random sparse code, replication-based code, and regular low density parity check (LDPC) code are also investigated. Simulations in several multi-robot problems demonstrate the promising performance of the proposed framework.
Federated learning (FL) is a machine learning setting where many clients (e.g. mobile devices or whole organizations) collaboratively train a model under the orchestration of a central server (e.g. service provider), while keeping the training data decentralized. FL embodies the principles of focused data collection and minimization, and can mitigate many of the systemic privacy risks and costs resulting from traditional, centralized machine learning and data science approaches. Motivated by the explosive growth in FL research, this paper discusses recent advances and presents an extensive collection of open problems and challenges.
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