Sihan Zeng

Sihan Zeng, Thinh T. Doan, Justin Romberg

We study the problem of finding the Nash equilibrium in a two-player zero-sum Markov game. Due to its formulation as a minimax optimization program, a natural approach to solve the problem is to perform gradient descent/ascent with respect to each player in an alternating fashion. However, due to the non-convexity/non-concavity of the underlying objective function, theoretical understandings of this method are limited. In our paper, we consider solving an entropy-regularized variant of the Markov game. The regularization introduces structure into the optimization landscape that make the solutions more identifiable and allow the problem to be solved more efficiently. Our main contribution is to show that under proper choices of the regularization parameter, the gradient descent ascent algorithm converges to the Nash equilibrium of the original unregularized problem. We explicitly characterize the finite-time performance of the last iterate of our algorithm, which vastly improves over the existing convergence bound of the gradient descent ascent algorithm without regularization. Finally, we complement the analysis with numerical simulations that illustrate the accelerated convergence of the algorithm.

Sihan Zeng, Thinh T. Doan, Justin Romberg

The aim of this paper is to improve the understanding of the optimization landscape for policy optimization problems in reinforcement learning. Specifically, we show that the superlevel set of the objective function with respect to the policy parameter is always a connected set both in the tabular setting and under policies represented by a class of neural networks. In addition, we show that the optimization objective as a function of the policy parameter and reward satisfies a stronger "equiconnectedness" property. To our best knowledge, these are novel and previously unknown discoveries. We present an application of the connectedness of these superlevel sets to the derivation of minimax theorems for robust reinforcement learning. We show that any minimax optimization program which is convex on one side and is equiconnected on the other side observes the minimax equality (i.e. has a Nash equilibrium). We find that this exact structure is exhibited by an interesting robust reinforcement learning problem under an adversarial reward attack, and the validity of its minimax equality immediately follows. This is the first time such a result is established in the literature.

Parisa Hassanzadeh, Eleonora Kreacic, Sihan Zeng et al.

We study the sequential decision-making problem of allocating a limited resource to agents that reveal their stochastic demands on arrival over a finite horizon. Our goal is to design fair allocation algorithms that exhaust the available resource budget. This is challenging in sequential settings where information on future demands is not available at the time of decision-making. We formulate the problem as a discrete time Markov decision process (MDP). We propose a new algorithm, SAFFE, that makes fair allocations with respect to the entire demands revealed over the horizon by accounting for expected future demands at each arrival time. The algorithm introduces regularization which enables the prioritization of current revealed demands over future potential demands depending on the uncertainty in agents' future demands. Using the MDP formulation, we show that SAFFE optimizes allocations based on an upper bound on the Nash Social Welfare fairness objective, and we bound its gap to optimality with the use of concentration bounds on total future demands. Using synthetic and real data, we compare the performance of SAFFE against existing approaches and a reinforcement learning policy trained on the MDP. We show that SAFFE leads to more fair and efficient allocations and achieves close-to-optimal performance in settings with dense arrivals.

Sihan Zeng, Sujay Bhatt, Eleonora Kreacic et al.

We consider the design of mechanisms that allocate limited resources among self-interested agents using neural networks. Unlike the recent works that leverage machine learning for revenue maximization in auctions, we consider welfare maximization as the key objective in the payment-free setting. Without payment exchange, it is unclear how we can align agents' incentives to achieve the desired objectives of truthfulness and social welfare simultaneously, without resorting to approximations. Our work makes novel contributions by designing an approximate mechanism that desirably trade-off social welfare with truthfulness. Specifically, (i) we contribute a new end-to-end neural network architecture, ExS-Net, that accommodates the idea of "money-burning" for mechanism design without payments; (ii)~we provide a generalization bound that guarantees the mechanism performance when trained under finite samples; and (iii) we provide an experimental demonstration of the merits of the proposed mechanism.

Sihan Zeng, Sujay Bhatt, Sumitra Ganesh

Neural networks are typically trained with a single learning rate across all layers. While recent empirical evidence suggests that assigning layer-specific learning rates can accelerate training, a principled understanding of the conditions and mechanisms under which non-uniform learning rates are beneficial remains limited. In this work, we investigate non-uniform learning rates through the lens of Stackelberg optimization. Specifically, we demonstrate that training neural networks with a smaller learning rate for the body layers and a larger learning rate for the final layer can be interpreted as a two-time-scale alternating gradient descent algorithm applied to a Stackelberg reformulation of the original objective. We establish finite-time convergence guarantees for the algorithm under broad conditions that accommodate constraint sets and non-smooth activation functions. Beyond convergence, we identify two mechanisms by which non-uniform learning rates can outperform uniform learning rates: (i) we show that certain problem instances induce a Stackelberg objective with stronger optimization structure than the original objective, yielding faster convergence to globally optimal solutions, (ii) our numerical analysis reveals that the Stackelberg objective can exhibit substantially sharper local curvature, especially in early training, which leads to more informative gradients and learning acceleration. Experiments in supervised learning and reinforcement learning support our findings.

Jung Yeon Park, Sujay Bhatt, Sihan Zeng et al.

Equivariant neural networks have shown great success in reinforcement learning, improving sample efficiency and generalization when there is symmetry in the task. However, in many problems, only approximate symmetry is present, which makes imposing exact symmetry inappropriate. Recently, approximately equivariant networks have been proposed for supervised classification and modeling physical systems. In this work, we develop approximately equivariant algorithms in reinforcement learning (RL). We define approximately equivariant MDPs and theoretically characterize the effect of approximate equivariance on the optimal $Q$ function. We propose novel RL architectures using relaxed group and steerable convolutions and experiment on several continuous control domains and stock trading with real financial data. Our results demonstrate that the approximately equivariant network performs on par with exactly equivariant networks when exact symmetries are present, and outperforms them when the domains exhibit approximate symmetry. As an added byproduct of these techniques, we observe increased robustness to noise at test time. Our code is available at https://github.com/jypark0/approx_equiv_rl.

Sihan Zeng, Sujay Bhatt, Alec Koppel et al.

The standard contextual bandit framework assumes fully observable and actionable contexts. In this work, we consider a new bandit setting with partially observable, correlated contexts and linear payoffs, motivated by the applications in finance where decision making is based on market information that typically displays temporal correlation and is not fully observed. We make the following contributions marrying ideas from statistical signal processing with bandits: (i) We propose an algorithmic pipeline named EMKF-Bandit, which integrates system identification, filtering, and classic contextual bandit algorithms into an iterative method alternating between latent parameter estimation and decision making. (ii) We analyze EMKF-Bandit when we select Thompson sampling as the bandit algorithm and show that it incurs a sub-linear regret under conditions on filtering. (iii) We conduct numerical simulations that demonstrate the benefits and practical applicability of the proposed pipeline.

Sihan Zeng, Sujay Bhatt, Sumitra Ganesh et al.

We study a structured bi-level optimization problem where the upper-level objective is a smooth function and the lower-level problem is policy optimization in a Markov decision process (MDP). The upper-level decision variable parameterizes the reward of the lower-level MDP, and the upper-level objective depends on the optimal induced policy. Existing methods for bi-level optimization and RL often require second-order information, impose strong regularization at the lower level, or inefficiently use samples through nested-loop procedures. In this work, we propose a single-loop, first-order actor-critic algorithm that optimizes the bi-level objective via a penalty-based reformulation. We introduce into the lower-level RL objective an attenuating entropy regularization, which enables asymptotically unbiased upper-level hyper-gradient estimation without solving the unregularized RL problem exactly. We establish the finite-time and finite-sample convergence of the proposed algorithm to a stationary point of the original, unregularized bi-level optimization problem through a novel lower-level residual analysis under a special type of Polyak-Lojasiewicz condition. We validate the performance of our method through experiments on a GridWorld goal position problem and on happy tweet generation through reinforcement learning from human feedback (RLHF).

Mingfu Liang, Xi Liu, Rong Jin et al.

Ads recommendation is a prominent service of online advertising systems and has been actively studied. Recent studies indicate that scaling-up and advanced design of the recommendation model can bring significant performance improvement. However, with a larger model scale, such prior studies have a significantly increasing gap from industry as they often neglect two fundamental challenges in industrial-scale applications. First, training and inference budgets are restricted for the model to be served, exceeding which may incur latency and impair user experience. Second, large-volume data arrive in a streaming mode with data distributions dynamically shifting, as new users/ads join and existing users/ads leave the system. We propose the External Large Foundation Model (ExFM) framework to address the overlooked challenges. Specifically, we develop external distillation and a data augmentation system (DAS) to control the computational cost of training/inference while maintaining high performance. We design the teacher in a way like a foundation model (FM) that can serve multiple students as vertical models (VMs) to amortize its building cost. We propose Auxiliary Head and Student Adapter to mitigate the data distribution gap between FM and VMs caused by the streaming data issue. Comprehensive experiments on internal industrial-scale applications and public datasets demonstrate significant performance gain by ExFM.

Sihan Zeng, Thinh T. Doan

Two-time-scale optimization is a framework introduced in Zeng et al. (2024) that abstracts a range of policy evaluation and policy optimization problems in reinforcement learning (RL). Akin to bi-level optimization under a particular type of stochastic oracle, the two-time-scale optimization framework has an upper level objective whose gradient evaluation depends on the solution of a lower level problem, which is to find the root of a strongly monotone operator. In this work, we propose a new method for solving two-time-scale optimization that achieves significantly faster convergence than the prior arts. The key idea of our approach is to leverage an averaging step to improve the estimates of the operators in both lower and upper levels before using them to update the decision variables. These additional averaging steps eliminate the direct coupling between the main variables, enabling the accelerated performance of our algorithm. We characterize the finite-time convergence rates of the proposed algorithm under various conditions of the underlying objective function, including strong convexity, Polyak-Lojasiewicz condition, and general non-convexity. These rates significantly improve over the best-known complexity of the standard two-time-scale stochastic approximation algorithm. When applied to RL, we show how the proposed algorithm specializes to novel online sample-based methods that surpass or match the performance of the existing state of the art. Finally, we support our theoretical results with numerical simulations in RL.

Benjamin Patrick Evans, Sihan Zeng, Sumitra Ganesh et al.

Agent-based models (ABMs) are valuable for modelling complex, potentially out-of-equilibria scenarios. However, ABMs have long suffered from the Lucas critique, stating that agent behaviour should adapt to environmental changes. Furthermore, the environment itself often adapts to these behavioural changes, creating a complex bi-level adaptation problem. Recent progress integrating multi-agent reinforcement learning into ABMs introduces adaptive agent behaviour, beginning to address the first part of this critique, however, the approaches are still relatively ad hoc, lacking a general formulation, and furthermore, do not tackle the second aspect of simultaneously adapting environmental level characteristics in addition to the agent behaviours. In this work, we develop a generic two-layer framework for ADaptive AGEnt based modelling (ADAGE) for addressing these problems. This framework formalises the bi-level problem as a Stackelberg game with conditional behavioural policies, providing a consolidated framework for adaptive agent-based modelling based on solving a coupled set of non-linear equations. We demonstrate how this generic approach encapsulates several common (previously viewed as distinct) ABM tasks, such as policy design, calibration, scenario generation, and robust behavioural learning under one unified framework. We provide example simulations on multiple complex economic and financial environments, showing the strength of the novel framework under these canonical settings, addressing long-standing critiques of traditional ABMs.

Sihan Zeng, Youngdae Kim, Yuxuan Ren et al.

At the heart of power system operations, alternating current optimal power flow (ACOPF) studies the generation of electric power in the most economical way under network-wide load requirement, and can be formulated as a highly structured non-convex quadratically constrained quadratic program (QCQP). Optimization-based solutions to ACOPF (such as ADMM or interior-point method), as the classic approach, require large amount of computation and cannot meet the need to repeatedly solve the problem as load requirement frequently changes. On the other hand, learning-based methods that directly predict the ACOPF solution given the load input incur little computational cost but often generates infeasible solutions (i.e. violate the constraints of ACOPF). In this work, we combine the best of both worlds -- we propose an innovated framework for learning ACOPF, where the input load is mapped to the ACOPF solution through a neural network in a computationally efficient and reliable manner. Key to our innovation is a specific-purpose "activation function" defined implicitly by a QCQP and a novel loss, which enforce constraint satisfaction. We show through numerical simulations that our proposed method achieves superior feasibility rate and generation cost in situations where the existing learning-based approaches fail.

Seo Taek Kong, Sihan Zeng, Thinh T. Doan et al.

We consider linear two-time-scale stochastic approximation algorithms driven by martingale noise. Recent applications in machine learning motivate the need to understand finite-time error rates, but conventional stochastic approximation analysis focus on either asymptotic convergence in distribution or finite-time bounds that are far from optimal. Prior work on asymptotic central limit theorems (CLTs) suggest that two-time-scale algorithms may be able to achieve $1/\sqrt{n}$ error in expectation, with a constant given by the expected norm of the limiting Gaussian vector. However, the best known finite-time rates are much slower. We derive the first non-asymptotic central limit theorem with respect to the Wasserstein-1 distance for two-time-scale stochastic approximation with Polyak-Ruppert averaging. As a corollary, we show that expected error achieved by Polyak-Ruppert averaging decays at rate $1/\sqrt{n}$, which significantly improves on the rates of convergence in prior works.

Deepeka Garg, Sihan Zeng, Sumitra Ganesh et al.

In this paper, we address the challenges of managing Standard Operating Procedures (SOPs), which often suffer from inconsistencies in language, format, and execution, leading to operational inefficiencies. Traditional process modeling demands significant manual effort, domain expertise, and familiarity with complex languages like Business Process Modeling Notation (BPMN), creating barriers for non-techincal users. We introduce SOP Structuring (SOPStruct), a novel approach that leverages Large Language Models (LLMs) to transform SOPs into decision-tree-based structured representations. SOPStruct produces a standardized representation of SOPs across different domains, reduces cognitive load, and improves user comprehension by effectively capturing task dependencies and ensuring sequential integrity. Our approach enables leveraging the structured information to automate workflows as well as empower the human users. By organizing procedures into logical graphs, SOPStruct facilitates backtracking and error correction, offering a scalable solution for process optimization. We employ a novel evaluation framework, combining deterministic methods with the Planning Domain Definition Language (PDDL) to verify graph soundness, and non-deterministic assessment by an LLM to ensure completeness. We empirically validate the robustness of our LLM-based structured SOP representation methodology across SOPs from different domains and varying levels of complexity. Despite the current lack of automation readiness in many organizations, our research highlights the transformative potential of LLMs to streamline process modeling, paving the way for future advancements in automated procedure optimization.

Yitao Bai, Sihan Zeng, Justin Romberg et al.

We study policy evaluation problems in multi-task reinforcement learning (RL) under a low-rank representation setting. In this setting, we are given $N$ learning tasks where the corresponding value function of these tasks lie in an $r$-dimensional subspace, with $r<N$. One can apply the classic temporal-difference (TD) learning method for solving these problems where this method learns the value function of each task independently. In this paper, we are interested in understanding whether one can exploit the low-rank structure of the multi-task setting to accelerate the performance of TD learning. To answer this question, we propose a new variant of TD learning method, where we integrate the so-called truncated singular value decomposition step into the update of TD learning. This additional step will enable TD learning to exploit the dominant directions due to the low rank structure to update the iterates, therefore, improving its performance. Our empirical results show that the proposed method significantly outperforms the classic TD learning, where the performance gap increases as the rank $r$ decreases. From the theoretical point of view, introducing the truncated singular value decomposition step into TD learning might cause an instability on the updates. We provide a theoretical result showing that the instability does not happen. Specifically, we prove that the proposed method converges at a rate $\mathcal{O}(\frac{\ln(t)}{t})$, where $t$ is the number of iterations. This rate matches that of the standard TD learning.

Deepeka Garg, Sihan Zeng, Annapoorani L. Narayanan et al.

Learning to autonomously execute long-horizon procedures from natural language remains a core challenge for intelligent agents. Free-form instructions such as recipes, scientific protocols, or business workflows encode rich procedural knowledge, but their variability and lack of structure cause agents driven by large language models (LLMs) to drift or fail during execution. We introduce Procedure Aware DynaMic Execution (PADME), an agent framework that produces and exploits a graph-based representation of procedures. Unlike prior work that relies on manual graph construction or unstructured reasoning, PADME autonomously transforms procedural text into executable graphs that capture task dependencies, decision points, and reusable subroutines. Central to PADME is a two-phase methodology; Teach phase, which focuses on systematic structuring, enrichment with executable logic of procedures, followed by Execute phase, which enables dynamic execution in response to real-time inputs and environment feedback. This separation ensures quality assurance and scalability, allowing expert knowledge to be encoded once and reliably reused across varying contexts. The graph representation also provides an inductive bias that reduces error accumulation in long-horizon reasoning, underscoring the importance of structured procedure modeling for reliable agent-driven automation. Empirically, PADME achieves state-of-the-art performance on four diverse benchmarks, including ALFWorld and ScienceWorld. These results demonstrate that agents equipped with graph-based procedure representations offer a powerful intermediate abstraction for robust and generalizable execution.

Sihan Zeng, Benjamin Patrick Evans, Sujay Bhatt et al.

We study policy optimization in Stackelberg mean field games (MFGs), a hierarchical framework for modeling the strategic interaction between a single leader and an infinitely large population of homogeneous followers. The objective can be formulated as a structured bi-level optimization problem, in which the leader needs to learn a policy maximizing its reward, anticipating the response of the followers. Existing methods for solving these (and related) problems often rely on restrictive independence assumptions between the leader's and followers' objectives, use samples inefficiently due to nested-loop algorithm structure, and lack finite-time convergence guarantees. To address these limitations, we propose AC-SMFG, a single-loop actor-critic algorithm that operates on continuously generated Markovian samples. The algorithm alternates between (semi-)gradient updates for the leader, a representative follower, and the mean field, and is simple to implement in practice. We establish the finite-time and finite-sample convergence of the algorithm to a stationary point of the Stackelberg objective. To our knowledge, this is the first Stackelberg MFG algorithm with non-asymptotic convergence guarantees. Our key assumption is a "gradient alignment" condition, which requires that the full policy gradient of the leader can be approximated by a partial component of it, relaxing the existing leader-follower independence assumption. Simulation results in a range of well-established economics environments demonstrate that AC-SMFG outperforms existing multi-agent and MFG learning baselines in policy quality and convergence speed.

Sihan Zeng, Sujay Bhatt, Alec Koppel et al.

Mechanism design in resource allocation studies dividing limited resources among self-interested agents whose satisfaction with the allocation depends on privately held utilities. We consider the problem in a payment-free setting, with the aim of maximizing social welfare while enforcing incentive compatibility (IC), i.e., agents cannot inflate allocations by misreporting their utilities. The well-known proportional fairness (PF) mechanism achieves the maximum possible social welfare but incurs an undesirably high exploitability (the maximum unilateral inflation in utility from misreport and a measure of deviation from IC). In fact, it is known that no mechanism can achieve the maximum social welfare and exact incentive compatibility (IC) simultaneously without the use of monetary incentives (Cole et al., 2013). Motivated by this fact, we propose learning an approximate mechanism that desirably trades off the competing objectives. Our main contribution is to design an innovative neural network architecture tailored to the resource allocation problem, which we name Regularized Proportional Fairness Network (RPF-Net). RPF-Net regularizes the output of the PF mechanism by a learned function approximator of the most exploitable allocation, with the aim of reducing the incentive for any agent to misreport. We derive generalization bounds that guarantee the mechanism performance when trained under finite and out-of-distribution samples and experimentally demonstrate the merits of the proposed mechanism compared to the state-of-the-art.

Sihan Zeng, Thinh T. Doan, Justin Romberg

Multi-task reinforcement learning (RL) aims to find a single policy that effectively solves multiple tasks at the same time. This paper presents a constrained formulation for multi-task RL where the goal is to maximize the average performance of the policy across tasks subject to bounds on the performance in each task. We consider solving this problem both in the centralized setting, where information for all tasks is accessible to a single server, and in the decentralized setting, where a network of agents, each given one task and observing local information, cooperate to find the solution of the globally constrained objective using local communication. We first propose a primal-dual algorithm that provably converges to the globally optimal solution of this constrained formulation under exact gradient evaluations. When the gradient is unknown, we further develop a sampled-based actor-critic algorithm that finds the optimal policy using online samples of state, action, and reward. Finally, we study the extension of the algorithm to the linear function approximation setting.

Sihan Zeng, Alyssa Kody, Youngdae Kim et al.

With the increasing penetration of distributed energy resources, distributed optimization algorithms have attracted significant attention for power systems applications due to their potential for superior scalability, privacy, and robustness to a single point-of-failure. The Alternating Direction Method of Multipliers (ADMM) is a popular distributed optimization algorithm; however, its convergence performance is highly dependent on the selection of penalty parameters, which are usually chosen heuristically. In this work, we use reinforcement learning (RL) to develop an adaptive penalty parameter selection policy for the AC optimal power flow (ACOPF) problem solved via ADMM with the goal of minimizing the number of iterations until convergence. We train our RL policy using deep Q-learning, and show that this policy can result in significantly accelerated convergence (up to a 59% reduction in the number of iterations compared to existing, curvature-informed penalty parameter selection methods). Furthermore, we show that our RL policy demonstrates promise for generalizability, performing well under unseen loading schemes as well as under unseen losses of lines and generators (up to a 50% reduction in iterations). This work thus provides a proof-of-concept for using RL for parameter selection in ADMM for power systems applications.

Sihan Zeng, Thinh T. Doan, Justin Romberg

We consider a discounted cost constrained Markov decision process (CMDP) policy optimization problem, in which an agent seeks to maximize a discounted cumulative reward subject to a number of constraints on discounted cumulative utilities. To solve this constrained optimization program, we study an online actor-critic variant of a classic primal-dual method where the gradients of both the primal and dual functions are estimated using samples from a single trajectory generated by the underlying time-varying Markov processes. This online primal-dual natural actor-critic algorithm maintains and iteratively updates three variables: a dual variable (or Lagrangian multiplier), a primal variable (or actor), and a critic variable used to estimate the gradients of both primal and dual variables. These variables are updated simultaneously but on different time scales (using different step sizes) and they are all intertwined with each other. Our main contribution is to derive a finite-time analysis for the convergence of this algorithm to the global optimum of a CMDP problem. Specifically, we show that with a proper choice of step sizes the optimality gap and constraint violation converge to zero in expectation at a rate $\mathcal{O}(1/K^{1/6})$, where K is the number of iterations. To our knowledge, this paper is the first to study the finite-time complexity of an online primal-dual actor-critic method for solving a CMDP problem. We also validate the effectiveness of this algorithm through numerical simulations.

Sihan Zeng, Thinh T. Doan, Justin Romberg

We study a new two-time-scale stochastic gradient method for solving optimization problems, where the gradients are computed with the aid of an auxiliary variable under samples generated by time-varying MDPs controlled by the underlying optimization variable. These time-varying samples make gradient directions in our update biased and dependent, which can potentially lead to the divergence of the iterates. In our two-time-scale approach, one scale is to estimate the true gradient from these samples, which is then used to update the estimate of the optimal solution. While these two iterates are implemented simultaneously, the former is updated "faster" than the latter. Our first contribution is to characterize the finite-time complexity of the proposed two-time-scale stochastic gradient method. In particular, we provide explicit formulas for the convergence rates of this method under different structural assumptions, namely, strong convexity, PL condition, and general non-convexity. We apply our framework to various policy optimization problems. First, we look at the infinite-horizon average-reward MDP with finite state and action spaces and derive a convergence rate of $O(k^{-2/5})$ for the online actor-critic algorithm under function approximation, which recovers the best known rate derived specifically for this problem. Second, we study the linear-quadratic regulator and show that an online actor-critic method converges with rate $O(k^{-2/3})$. Third, we use the actor-critic algorithm to solve the policy optimization problem in an entropy regularized Markov decision process, where we also establish a convergence of $O(k^{-2/3})$. The results we derive for both the second and third problem are novel and previously unknown in the literature. Finally, we briefly present the application of our framework to gradient-based policy evaluation algorithms in reinforcement learning.

Sihan Zeng, Thinh T. Doan, Justin Romberg

We study a decentralized variant of stochastic approximation, a data-driven approach for finding the root of an operator under noisy measurements. A network of agents, each with its own operator and data observations, cooperatively find the fixed point of the aggregate operator over a decentralized communication graph. Our main contribution is to provide a finite-time analysis of this decentralized stochastic approximation method when the data observed at each agent are sampled from a Markov process; this lack of independence makes the iterates biased and (potentially) unbounded. Under fairly standard assumptions, we show that the convergence rate of the proposed method is essentially the same as if the samples were independent, differing only by a log factor that accounts for the mixing time of the Markov processes. The key idea in our analysis is to introduce a novel Razumikhin-Lyapunov function, motivated by the one used in analyzing the stability of delayed ordinary differential equations. We also discuss applications of the proposed method on a number of interesting learning problems in multi-agent systems.

Sihan Zeng, Aqeel Anwar, Thinh Doan et al.

We develop a mathematical framework for solving multi-task reinforcement learning (MTRL) problems based on a type of policy gradient method. The goal in MTRL is to learn a common policy that operates effectively in different environments; these environments have similar (or overlapping) state spaces, but have different rewards and dynamics. We highlight two fundamental challenges in MTRL that are not present in its single task counterpart, and illustrate them with simple examples. We then develop a decentralized entropy-regularized policy gradient method for solving the MTRL problem, and study its finite-time convergence rate. We demonstrate the effectiveness of the proposed method using a series of numerical experiments. These experiments range from small-scale "GridWorld" problems that readily demonstrate the trade-offs involved in multi-task learning to large-scale problems, where common policies are learned to navigate an airborne drone in multiple (simulated) environments.

Shaojie Xu, Sihan Zeng, Justin Romberg

Deep learning models have significantly improved the visual quality and accuracy on compressive sensing recovery. In this paper, we propose an algorithm for signal reconstruction from compressed measurements with image priors captured by a generative model. We search and constrain on latent variable space to make the method stable when the number of compressed measurements is extremely limited. We show that, by exploiting certain structures of the latent variables, the proposed method produces improved reconstruction accuracy and preserves realistic and non-smooth features in the image. Our algorithm achieves high computation speed by projecting between the original signal space and the latent variable space in an alternating fashion.