Policy learning in multi-agent reinforcement learning (MARL) is challenging due to the exponential growth of joint state-action space with respect to the number of agents. To achieve higher scalability, the paradigm of centralized training with decentralized execution (CTDE) is broadly adopted with factorized structure in MARL. However, we observe that existing CTDE algorithms in cooperative MARL cannot achieve optimality even in simple matrix games. To understand this phenomenon, we introduce a framework of Generalized Multi-Agent Actor-Critic with Policy Factorization (GPF-MAC), which characterizes the learning of factorized joint policies, i.e., each agent's policy only depends on its own observation-action history. We show that most popular CTDE MARL algorithms are special instances of GPF-MAC and may be stuck in a suboptimal joint policy. To address this issue, we present a novel transformation framework that reformulates a multi-agent MDP as a special "single-agent" MDP with a sequential structure and can allow employing off-the-shelf single-agent reinforcement learning (SARL) algorithms to efficiently learn corresponding multi-agent tasks. This transformation retains the optimality guarantee of SARL algorithms into cooperative MARL. To instantiate this transformation framework, we propose a Transformed PPO, called T-PPO, which can theoretically perform optimal policy learning in the finite multi-agent MDPs and shows significant outperformance on a large set of cooperative multi-agent tasks.
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The age of information metric fails to correctly describe the intrinsic semantics of a status update. In an intelligent reflecting surface-aided cooperative relay communication system, we propose the age of semantics (AoS) for measuring semantics freshness of the status updates. Specifically, we focus on the status updating from a source node (SN) to the destination, which is formulated as a Markov decision process (MDP). The objective of the SN is to maximize the expected satisfaction of AoS and energy consumption under the maximum transmit power constraint. To seek the optimal control policy, we first derive an online deep actor-critic (DAC) learning scheme under the on-policy temporal difference learning framework. However, implementing the online DAC in practice poses the key challenge in infinitely repeated interactions between the SN and the system, which can be dangerous particularly during the exploration. We then put forward a novel offline DAC scheme, which estimates the optimal control policy from a previously collected dataset without any further interactions with the system. Numerical experiments verify the theoretical results and show that our offline DAC scheme significantly outperforms the online DAC scheme and the most representative baselines in terms of mean utility, demonstrating strong robustness to dataset quality.
Reaching a consensus in a swarm of robots is one of the fundamental problems in swarm robotics, examining the possibility of reaching an agreement within the swarm members. The recently-introduced contamination problem offers a new perspective of the problem, in which swarm members should reach a consensus in spite of the existence of adversarial members that intentionally act to divert the swarm members towards a different consensus. In this paper, we search for a consensus-reaching algorithm under the contamination problem setting by taking a top-down approach: We transform the problem to a centralized two-player game in which each player controls the behavior of a subset of the swarm, trying to force the entire swarm to converge to an agreement on its own value. We define a performance metric for each players performance, proving a correlation between this metric and the chances of the player to win the game. We then present the globally optimal solution to the game and prove that unfortunately it is unattainable in a distributed setting, due to the challenging characteristics of the swarm members. We therefore examine the problem on a simplified swarm model, and compare the performance of the globally optimal strategy with locally optimal strategies, demonstrating its superiority in rigorous simulation experiments.
Using information-theoretic principles, we consider the generalization error (gen-error) of iterative semi-supervised learning (SSL) algorithms that iteratively generate pseudo-labels for a large amount of unlabelled data to progressively refine the model parameters. In contrast to most previous works that {\em bound} the gen-error, we provide an {\em exact} expression for the gen-error and particularize it to the binary Gaussian mixture model. Our theoretical results suggest that when the class conditional variances are not too large, the gen-error decreases with the number of iterations, but quickly saturates. On the flip side, if the class conditional variances (and so amount of overlap between the classes) are large, the gen-error increases with the number of iterations. To mitigate this undesirable effect, we show that regularization can reduce the gen-error. The theoretical results are corroborated by extensive experiments on the MNIST and CIFAR datasets in which we notice that for easy-to-distinguish classes, the gen-error improves after several pseudo-labelling iterations, but saturates afterwards, and for more difficult-to-distinguish classes, regularization improves the generalization performance.
Feature transformation aims to extract a good representation (feature) space by mathematically transforming existing features. It is crucial to address the curse of dimensionality, enhance model generalization, overcome data sparsity, and expand the availability of classic models. Current research focuses on domain knowledge-based feature engineering or learning latent representations; nevertheless, these methods are not entirely automated and cannot produce a traceable and optimal representation space. When rebuilding a feature space for a machine learning task, can these limitations be addressed concurrently? In this extension study, we present a self-optimizing framework for feature transformation. To achieve a better performance, we improved the preliminary work by (1) obtaining an advanced state representation for enabling reinforced agents to comprehend the current feature set better; and (2) resolving Q-value overestimation in reinforced agents for learning unbiased and effective policies. Finally, to make experiments more convincing than the preliminary work, we conclude by adding the outlier detection task with five datasets, evaluating various state representation approaches, and comparing different training strategies. Extensive experiments and case studies show that our work is more effective and superior.
We study online learning problems in which a decision maker has to take a sequence of decisions subject to $m$ long-term constraints. The goal of the decision maker is to maximize their total reward, while at the same time achieving small cumulative constraints violation across the $T$ rounds. We present the first best-of-both-world type algorithm for this general class of problems, with no-regret guarantees both in the case in which rewards and constraints are selected according to an unknown stochastic model, and in the case in which they are selected at each round by an adversary. Our algorithm is the first to provide guarantees in the adversarial setting with respect to the optimal fixed strategy that satisfies the long-term constraints. In particular, it guarantees a $\rho/(1+\rho)$ fraction of the optimal reward and sublinear regret, where $\rho$ is a feasibility parameter related to the existence of strictly feasible solutions. Our framework employs traditional regret minimizers as black-box components. Therefore, by instantiating it with an appropriate choice of regret minimizers it can handle the full-feedback as well as the bandit-feedback setting. Moreover, it allows the decision maker to seamlessly handle scenarios with non-convex rewards and constraints. We show how our framework can be applied in the context of budget-management mechanisms for repeated auctions in order to guarantee long-term constraints that are not packing (e.g., ROI constraints).
Mean-Field Control (MFC) has recently been proven to be a scalable tool to approximately solve large-scale multi-agent reinforcement learning (MARL) problems. However, these studies are typically limited to unconstrained cumulative reward maximization framework. In this paper, we show that one can use the MFC approach to approximate the MARL problem even in the presence of constraints. Specifically, we prove that, an $N$-agent constrained MARL problem, with state, and action spaces of each individual agents being of sizes $|\mathcal{X}|$, and $|\mathcal{U}|$ respectively, can be approximated by an associated constrained MFC problem with an error, $e\triangleq \mathcal{O}\left([\sqrt{|\mathcal{X}|}+\sqrt{|\mathcal{U}|}]/\sqrt{N}\right)$. In a special case where the reward, cost, and state transition functions are independent of the action distribution of the population, we prove that the error can be improved to $e=\mathcal{O}(\sqrt{|\mathcal{X}|}/\sqrt{N})$. Also, we provide a Natural Policy Gradient based algorithm and prove that it can solve the constrained MARL problem within an error of $\mathcal{O}(e)$ with a sample complexity of $\mathcal{O}(e^{-6})$.
Emerging quantum algorithms for problems such as element distinctness, subset sum, and closest pair demonstrate computational advantages by relying on abstract data structures. Practically realizing such an algorithm as a program for a quantum computer requires an efficient implementation of the data structure whose operations correspond to unitary operators that manipulate quantum superpositions of data. To correctly operate in superposition, an implementation must satisfy three properties -- reversibility, history independence, and bounded-time execution. Standard implementations, such as the representation of an abstract set as a hash table, fail these properties, calling for tools to develop specialized implementations. In this work, we present Core Tower, the first language for quantum programming with random-access memory. Core Tower enables the developer to implement data structures as pointer-based, linked data. It features a reversible semantics enabling every valid program to be translated to a unitary quantum circuit. We present Boson, the first memory allocator that supports reversible, history-independent, and constant-time dynamic memory allocation in quantum superposition. We also present Tower, a language for quantum programming with recursively defined data structures. Tower features a type system that bounds all recursion using classical parameters as is necessary for a program to execute on a quantum computer. Using Tower, we implement Ground, the first quantum library of data structures, including lists, stacks, queues, strings, and sets. We provide the first executable implementation of sets that satisfies all three mandated properties of reversibility, history independence, and bounded-time execution.
Bid optimization for online advertising from single advertiser's perspective has been thoroughly investigated in both academic research and industrial practice. However, existing work typically assume competitors do not change their bids, i.e., the wining price is fixed, leading to poor performance of the derived solution. Although a few studies use multi-agent reinforcement learning to set up a cooperative game, they still suffer the following drawbacks: (1) They fail to avoid collusion solutions where all the advertisers involved in an auction collude to bid an extremely low price on purpose. (2) Previous works cannot well handle the underlying complex bidding environment, leading to poor model convergence. This problem could be amplified when handling multiple objectives of advertisers which are practical demands but not considered by previous work. In this paper, we propose a novel multi-objective cooperative bid optimization formulation called Multi-Agent Cooperative bidding Games (MACG). MACG sets up a carefully designed multi-objective optimization framework where different objectives of advertisers are incorporated. A global objective to maximize the overall profit of all advertisements is added in order to encourage better cooperation and also to protect self-bidding advertisers. To avoid collusion, we also introduce an extra platform revenue constraint. We analyze the optimal functional form of the bidding formula theoretically and design a policy network accordingly to generate auction-level bids. Then we design an efficient multi-agent evolutionary strategy for model optimization. Offline experiments and online A/B tests conducted on the Taobao platform indicate both single advertiser's objective and global profit have been significantly improved compared to state-of-art methods.
With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.
In structure learning, the output is generally a structure that is used as supervision information to achieve good performance. Considering the interpretation of deep learning models has raised extended attention these years, it will be beneficial if we can learn an interpretable structure from deep learning models. In this paper, we focus on Recurrent Neural Networks (RNNs) whose inner mechanism is still not clearly understood. We find that Finite State Automaton (FSA) that processes sequential data has more interpretable inner mechanism and can be learned from RNNs as the interpretable structure. We propose two methods to learn FSA from RNN based on two different clustering methods. We first give the graphical illustration of FSA for human beings to follow, which shows the interpretability. From the FSA's point of view, we then analyze how the performance of RNNs are affected by the number of gates, as well as the semantic meaning behind the transition of numerical hidden states. Our results suggest that RNNs with simple gated structure such as Minimal Gated Unit (MGU) is more desirable and the transitions in FSA leading to specific classification result are associated with corresponding words which are understandable by human beings.
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