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We present a methodology to automatically compute worst-case performance bounds for a large class of first-order decentralized optimization algorithms. These algorithms aim at minimizing the average of local functions that are distributed across a network of agents. They typically combine local computations and consensus steps. Our methodology is based on the approach of Performance Estimation Problem (PEP), which allows computing the worst-case performance and a worst-case instance of first-order optimization algorithms by solving an SDP. We propose two ways of representing consensus steps in PEPs, which allow writing and solving PEPs for decentralized optimization. The first formulation is exact but specific to a given averaging matrix. The second formulation is a relaxation but provides guarantees valid over an entire class of averaging matrices, characterized by their spectral range. This formulation often allows recovering a posteriori the worst possible averaging matrix for the given algorithm. We apply our methodology to three different decentralized methods. For each of them, we obtain numerically tight worst-case performance bounds that significantly improve on the existing ones, as well as insights about the parameters tuning and the worst communication networks.

Sequential incentive marketing is an important approach for online businesses to acquire customers, increase loyalty and boost sales. How to effectively allocate the incentives so as to maximize the return (e.g., business objectives) under the budget constraint, however, is less studied in the literature. This problem is technically challenging due to the facts that 1) the allocation strategy has to be learned using historically logged data, which is counterfactual in nature, and 2) both the optimality and feasibility (i.e., that cost cannot exceed budget) needs to be assessed before being deployed to online systems. In this paper, we formulate the problem as a constrained Markov decision process (CMDP). To solve the CMDP problem with logged counterfactual data, we propose an efficient learning algorithm which combines bisection search and model-based planning. First, the CMDP is converted into its dual using Lagrangian relaxation, which is proved to be monotonic with respect to the dual variable. Furthermore, we show that the dual problem can be solved by policy learning, with the optimal dual variable being found efficiently via bisection search (i.e., by taking advantage of the monotonicity). Lastly, we show that model-based planing can be used to effectively accelerate the joint optimization process without retraining the policy for every dual variable. Empirical results on synthetic and real marketing datasets confirm the effectiveness of our methods.

The chain graph model admits both undirected and directed edges in one graph, where symmetric conditional dependencies are encoded via undirected edges and asymmetric causal relations are encoded via directed edges. Though frequently encountered in practice, the chain graph model has been largely under investigated in literature, possibly due to the lack of identifiability conditions between undirected and directed edges. In this paper, we first establish a set of novel identifiability conditions for the Gaussian chain graph model, exploiting a low rank plus sparse decomposition of the precision matrix. Further, an efficient learning algorithm is built upon the identifiability conditions to fully recover the chain graph structure. Theoretical analysis on the proposed method is conducted, assuring its asymptotic consistency in recovering the exact chain graph structure. The advantage of the proposed method is also supported by numerical experiments on both simulated examples and a real application on the Standard & Poor 500 index data.

The dynamic and evolutionary nature of service requirements in wireless networks has motivated the telecom industry to consider intelligent self-adapting Reinforcement Learning (RL) agents for controlling the growing portfolio of network services. Infusion of many new types of services is anticipated with future adoption of 6G networks, and sometimes these services will be defined by applications that are external to the network. An RL agent trained for managing the needs of a specific service type may not be ideal for managing a different service type without domain adaptation. We provide a simple heuristic for evaluating a measure of proximity between a new service and existing services, and show that the RL agent of the most proximal service rapidly adapts to the new service type through a well defined process of domain adaptation. Our approach enables a trained source policy to adapt to new situations with changed dynamics without retraining a new policy, thereby achieving significant computing and cost-effectiveness. Such domain adaptation techniques may soon provide a foundation for more generalized RL-based service management under the face of rapidly evolving service types.

Motivated by applications such as machine repair, project monitoring, and anti-poaching patrol scheduling, we study intervention planning of stochastic processes under resource constraints. This planning problem has previously been modeled as restless multi-armed bandits (RMAB), where each arm is an intervention-dependent Markov Decision Process. However, the existing literature assumes all intervention resources belong to a single uniform pool, limiting their applicability to real-world settings where interventions are carried out by a set of workers, each with their own costs, budgets, and intervention effects. In this work, we consider a novel RMAB setting, called multi-worker restless bandits (MWRMAB) with heterogeneous workers. The goal is to plan an intervention schedule that maximizes the expected reward while satisfying budget constraints on each worker as well as fairness in terms of the load assigned to each worker. Our contributions are two-fold: (1) we provide a multi-worker extension of the Whittle index to tackle heterogeneous costs and per-worker budget and (2) we develop an index-based scheduling policy to achieve fairness. Further, we evaluate our method on various cost structures and show that our method significantly outperforms other baselines in terms of fairness without sacrificing much in reward accumulated.

Large language models (LLMs) trained on code completion have been shown to be capable of synthesizing simple Python programs from docstrings [1]. We find that these code-writing LLMs can be re-purposed to write robot policy code, given natural language commands. Specifically, policy code can express functions or feedback loops that process perception outputs (e.g.,from object detectors [2], [3]) and parameterize control primitive APIs. When provided as input several example language commands (formatted as comments) followed by corresponding policy code (via few-shot prompting), LLMs can take in new commands and autonomously re-compose API calls to generate new policy code respectively. By chaining classic logic structures and referencing third-party libraries (e.g., NumPy, Shapely) to perform arithmetic, LLMs used in this way can write robot policies that (i) exhibit spatial-geometric reasoning, (ii) generalize to new instructions, and (iii) prescribe precise values (e.g., velocities) to ambiguous descriptions ("faster") depending on context (i.e., behavioral commonsense). This paper presents code as policies: a robot-centric formulation of language model generated programs (LMPs) that can represent reactive policies (e.g., impedance controllers), as well as waypoint-based policies (vision-based pick and place, trajectory-based control), demonstrated across multiple real robot platforms. Central to our approach is prompting hierarchical code-gen (recursively defining undefined functions), which can write more complex code and also improves state-of-the-art to solve 39.8% of problems on the HumanEval [1] benchmark. Code and videos are available at //code-as-policies.github.io

AlphaZero is a self-play reinforcement learning algorithm that achieves superhuman play in chess, shogi, and Go via policy iteration. To be an effective policy improvement operator, AlphaZero's search requires accurate value estimates for the states appearing in its search tree. AlphaZero trains upon self-play matches beginning from the initial state of a game and only samples actions over the first few moves, limiting its exploration of states deeper in the game tree. We introduce Go-Exploit, a novel search control strategy for AlphaZero. Go-Exploit samples the start state of its self-play trajectories from an archive of states of interest. Beginning self-play trajectories from varied starting states enables Go-Exploit to more effectively explore the game tree and to learn a value function that generalizes better. Producing shorter self-play trajectories allows Go-Exploit to train upon more independent value targets, improving value training. Finally, the exploration inherent in Go-Exploit reduces its need for exploratory actions, enabling it to train under more exploitative policies. In the games of Connect Four and 9x9 Go, we show that Go-Exploit learns with a greater sample efficiency than standard AlphaZero, resulting in stronger performance against reference opponents and in head-to-head play. We also compare Go-Exploit to KataGo, a more sample efficient reimplementation of AlphaZero, and demonstrate that Go-Exploit has a more effective search control strategy. Furthermore, Go-Exploit's sample efficiency improves when KataGo's other innovations are incorporated.

We study optimality for the safety-constrained Markov decision process which is the underlying framework for safe reinforcement learning. Specifically, we consider a constrained Markov decision process (with finite states and finite actions) where the goal of the decision maker is to reach a target set while avoiding an unsafe set(s) with certain probabilistic guarantees. Therefore the underlying Markov chain for any control policy will be multichain since by definition there exists a target set and an unsafe set. The decision maker also has to be optimal (with respect to a cost function) while navigating to the target set. This gives rise to a multi-objective optimization problem. We highlight the fact that Bellman's principle of optimality may not hold for constrained Markov decision problems with an underlying multichain structure (as shown by the counterexample). We resolve the counterexample by formulating the aforementioned multi-objective optimization problem as a zero-sum game and thereafter construct an asynchronous value iteration scheme for the Lagrangian (similar to Shapley's algorithm. Finally, we consider the reinforcement learning problem for the same and construct a modified Q-learning algorithm for learning the Lagrangian from data. We also provide a lower bound on the number of iterations required for learning the Lagrangian and corresponding error bounds.

Solving analytically intractable partial differential equations (PDEs) that involve at least one variable defined on an unbounded domain arises in numerous physical applications. Accurately solving unbounded domain PDEs requires efficient numerical methods that can resolve the dependence of the PDE on the unbounded variable over at least several orders of magnitude. We propose a solution to such problems by combining two classes of numerical methods: (i) adaptive spectral methods and (ii) physics-informed neural networks (PINNs). The numerical approach that we develop takes advantage of the ability of physics-informed neural networks to easily implement high-order numerical schemes to efficiently solve PDEs and extrapolate numerical solutions at any point in space and time. We then show how recently introduced adaptive techniques for spectral methods can be integrated into PINN-based PDE solvers to obtain numerical solutions of unbounded domain problems that cannot be efficiently approximated by standard PINNs. Through a number of examples, we demonstrate the advantages of the proposed spectrally adapted PINNs in solving PDEs and estimating model parameters from noisy observations in unbounded domains.

Unsupervised domain adaptation has recently emerged as an effective paradigm for generalizing deep neural networks to new target domains. However, there is still enormous potential to be tapped to reach the fully supervised performance. In this paper, we present a novel active learning strategy to assist knowledge transfer in the target domain, dubbed active domain adaptation. We start from an observation that energy-based models exhibit free energy biases when training (source) and test (target) data come from different distributions. Inspired by this inherent mechanism, we empirically reveal that a simple yet efficient energy-based sampling strategy sheds light on selecting the most valuable target samples than existing approaches requiring particular architectures or computation of the distances. Our algorithm, Energy-based Active Domain Adaptation (EADA), queries groups of targe data that incorporate both domain characteristic and instance uncertainty into every selection round. Meanwhile, by aligning the free energy of target data compact around the source domain via a regularization term, domain gap can be implicitly diminished. Through extensive experiments, we show that EADA surpasses state-of-the-art methods on well-known challenging benchmarks with substantial improvements, making it a useful option in the open world. Code is available at //github.com/BIT-DA/EADA.