Alfredo García

Siliang Zeng, Mingyi Hong, Alfredo Garcia

We consider the task of estimating a structural model of dynamic decisions by a human agent based upon the observable history of implemented actions and visited states. This problem has an inherent nested structure: in the inner problem, an optimal policy for a given reward function is identified while in the outer problem, a measure of fit is maximized. Several approaches have been proposed to alleviate the computational burden of this nested-loop structure, but these methods still suffer from high complexity when the state space is either discrete with large cardinality or continuous in high dimensions. Other approaches in the inverse reinforcement learning (IRL) literature emphasize policy estimation at the expense of reduced reward estimation accuracy. In this paper we propose a single-loop estimation algorithm with finite time guarantees that is equipped to deal with high-dimensional state spaces without compromising reward estimation accuracy. In the proposed algorithm, each policy improvement step is followed by a stochastic gradient step for likelihood maximization. We show that the proposed algorithm converges to a stationary solution with a finite-time guarantee. Further, if the reward is parameterized linearly, we show that the algorithm approximates the maximum likelihood estimator sublinearly. Finally, by using robotics control problems in MuJoCo and their transfer settings, we show that the proposed algorithm achieves superior performance compared with other IRL and imitation learning benchmarks.

Siliang Zeng, Chenliang Li, Alfredo Garcia et al.

Inverse reinforcement learning (IRL) aims to recover the reward function and the associated optimal policy that best fits observed sequences of states and actions implemented by an expert. Many algorithms for IRL have an inherently nested structure: the inner loop finds the optimal policy given parametrized rewards while the outer loop updates the estimates towards optimizing a measure of fit. For high dimensional environments such nested-loop structure entails a significant computational burden. To reduce the computational burden of a nested loop, novel methods such as SQIL [1] and IQ-Learn [2] emphasize policy estimation at the expense of reward estimation accuracy. However, without accurate estimated rewards, it is not possible to do counterfactual analysis such as predicting the optimal policy under different environment dynamics and/or learning new tasks. In this paper we develop a novel single-loop algorithm for IRL that does not compromise reward estimation accuracy. In the proposed algorithm, each policy improvement step is followed by a stochastic gradient step for likelihood maximization. We show that the proposed algorithm provably converges to a stationary solution with a finite-time guarantee. If the reward is parameterized linearly, we show the identified solution corresponds to the solution of the maximum entropy IRL problem. Finally, by using robotics control problems in MuJoCo and their transfer settings, we show that the proposed algorithm achieves superior performance compared with other IRL and imitation learning benchmarks.

Ran Wei, Siliang Zeng, Chenliang Li et al.

We consider a Bayesian approach to offline model-based inverse reinforcement learning (IRL). The proposed framework differs from existing offline model-based IRL approaches by performing simultaneous estimation of the expert's reward function and subjective model of environment dynamics. We make use of a class of prior distributions which parameterizes how accurate the expert's model of the environment is to develop efficient algorithms to estimate the expert's reward and subjective dynamics in high-dimensional settings. Our analysis reveals a novel insight that the estimated policy exhibits robust performance when the expert is believed (a priori) to have a highly accurate model of the environment. We verify this observation in the MuJoCo environments and show that our algorithms outperform state-of-the-art offline IRL algorithms.

Ran Wei, Nathan Lambert, Anthony McDonald et al.

Model-based Reinforcement Learning (MBRL) aims to make agents more sample-efficient, adaptive, and explainable by learning an explicit model of the environment. While the capabilities of MBRL agents have significantly improved in recent years, how to best learn the model is still an unresolved question. The majority of MBRL algorithms aim at training the model to make accurate predictions about the environment and subsequently using the model to determine the most rewarding actions. However, recent research has shown that model predictive accuracy is often not correlated with action quality, tracing the root cause to the objective mismatch between accurate dynamics model learning and policy optimization of rewards. A number of interrelated solution categories to the objective mismatch problem have emerged as MBRL continues to mature as a research area. In this work, we provide an in-depth survey of these solution categories and propose a taxonomy to foster future research.

Siliang Zeng, Chenliang Li, Alfredo Garcia et al.

Offline inverse reinforcement learning (Offline IRL) aims to recover the structure of rewards and environment dynamics that underlie observed actions in a fixed, finite set of demonstrations from an expert agent. Accurate models of expertise in executing a task has applications in safety-sensitive applications such as clinical decision making and autonomous driving. However, the structure of an expert's preferences implicit in observed actions is closely linked to the expert's model of the environment dynamics (i.e. the ``world'' model). Thus, inaccurate models of the world obtained from finite data with limited coverage could compound inaccuracy in estimated rewards. To address this issue, we propose a bi-level optimization formulation of the estimation task wherein the upper level is likelihood maximization based upon a conservative model of the expert's policy (lower level). The policy model is conservative in that it maximizes reward subject to a penalty that is increasing in the uncertainty of the estimated model of the world. We propose a new algorithmic framework to solve the bi-level optimization problem formulation and provide statistical and computational guarantees of performance for the associated optimal reward estimator. Finally, we demonstrate that the proposed algorithm outperforms the state-of-the-art offline IRL and imitation learning benchmarks by a large margin, over the continuous control tasks in MuJoCo and different datasets in the D4RL benchmark.

Darpit Dave, Kathan Vyas, Jagadish Kumaran Jayagopal et al.

Continuous glucose monitoring (CGM) devices provide real-time glucose monitoring and timely alerts for glycemic excursions, improving glycemic control among patients with diabetes. However, identifying rare events like hypoglycemia and hyperglycemia remain challenging due to their infrequency. Moreover, limited access to sensitive patient data hampers the development of robust machine learning models. Our objective is to accurately predict glycemic excursions while addressing data privacy concerns. To tackle excursion prediction, we propose a novel Hypo-Hyper (HH) loss function, which significantly improves performance in the glycemic excursion regions. The HH loss function demonstrates a 46% improvement over mean-squared error (MSE) loss across 125 patients. To address privacy concerns, we propose FedGlu, a machine learning model trained in a federated learning (FL) framework. FL allows collaborative learning without sharing sensitive data by training models locally and sharing only model parameters across other patients. FedGlu achieves a 35% superior glycemic excursion detection rate compared to local models. This improvement translates to enhanced performance in predicting both, hypoglycemia and hyperglycemia, for 105 out of 125 patients. These results underscore the effectiveness of the proposed HH loss function in augmenting the predictive capabilities of glucose predictions. Moreover, implementing models within a federated learning framework not only ensures better predictive capabilities but also safeguards sensitive data concurrently.

Youbang Sun, Shixiang Chen, Alfredo Garcia et al.

In this paper, we investigate decentralized non-convex optimization with orthogonal constraints. Conventional algorithms for this setting require either manifold retractions or other types of projection to ensure feasibility, both of which involve costly linear algebra operations (e.g., SVD or matrix inversion). On the other hand, infeasible methods are able to provide similar performance with higher computational efficiency. Inspired by this, we propose the first decentralized version of the retraction-free landing algorithm, called \textbf{D}ecentralized \textbf{R}etraction-\textbf{F}ree \textbf{G}radient \textbf{T}racking (DRFGT). We theoretically prove that DRFGT enjoys the ergodic convergence rate of $\mathcal{O}(1/K)$, matching the convergence rate of centralized, retraction-based methods. We further establish that under a local Riemannian PŁ condition, DRFGT achieves a much faster linear convergence rate. Numerical experiments demonstrate that DRFGT performs on par with the state-of-the-art retraction-based methods with substantially reduced computational overhead.

Chenliang Li, Siliang Zeng, Zeyi Liao et al.

Aligning human preference and value is an important requirement for building contemporary foundation models and embodied AI. However, popular approaches such as reinforcement learning with human feedback (RLHF) break down the task into successive stages, such as supervised fine-tuning (SFT), reward modeling (RM), and reinforcement learning (RL), each performing one specific learning task. Such a sequential approach results in serious issues such as significant under-utilization of data and distribution mismatch between the learned reward model and generated policy, which eventually lead to poor alignment performance. We develop a single stage approach named Alignment with Integrated Human Feedback (AIHF), capable of integrating both human preference and demonstration to train reward models and the policy. The proposed approach admits a suite of efficient algorithms, which can easily reduce to, and leverage, popular alignment algorithms such as RLHF and Directly Policy Optimization (DPO), and only requires minor changes to the existing alignment pipelines. We demonstrate the efficiency of the proposed solutions with extensive experiments involving alignment problems in LLMs and robotic control problems in MuJoCo. We observe that the proposed solutions outperform the existing alignment algorithms such as RLHF and DPO by large margins, especially when the amount of high-quality preference data is relatively limited.

Jiachen Xi, Alfredo Garcia, Petar Momcilovic

Regularized Markov Decision Processes serve as models of sequential decision making under uncertainty wherein the decision maker has limited information processing capacity and/or aversion to model ambiguity. With functional approximation, the convergence properties of learning algorithms for regularized MDPs (e.g. soft Q-learning) are not well understood because the composition of the regularized Bellman operator and a projection onto the span of basis vectors is not a contraction with respect to any norm. In this paper, we consider a bi-level optimization formulation of regularized Q-learning with linear functional approximation. The {\em lower} level optimization problem aims to identify a value function approximation that satisfies Bellman's recursive optimality condition and the {\em upper} level aims to find the projection onto the span of basis vectors. This formulation motivates a single-loop algorithm with finite time convergence guarantees. The algorithm operates on two time-scales: updates to the projection of state-action values are `slow' in that they are implemented with a step size that is smaller than the one used for `faster' updates of approximate solutions to Bellman's recursive optimality equation. We show that, under certain assumptions, the proposed algorithm converges to a stationary point in the presence of Markovian noise. In addition, we provide a performance guarantee for the policies derived from the proposed algorithm.

Siliang Zeng, Tianyi Chen, Alfredo Garcia et al.

Multi-agent reinforcement learning (MARL) has attracted much research attention recently. However, unlike its single-agent counterpart, many theoretical and algorithmic aspects of MARL have not been well-understood. In this paper, we study the emergence of coordinated behavior by autonomous agents using an actor-critic (AC) algorithm. Specifically, we propose and analyze a class of coordinated actor-critic algorithms (CAC) in which individually parametrized policies have a {\it shared} part (which is jointly optimized among all agents) and a {\it personalized} part (which is only locally optimized). Such kind of {\it partially personalized} policy allows agents to learn to coordinate by leveraging peers' past experience and adapt to individual tasks. The flexibility in our design allows the proposed MARL-CAC algorithm to be used in a {\it fully decentralized} setting, where the agents can only communicate with their neighbors, as well as a {\it federated} setting, where the agents occasionally communicate with a server while optimizing their (partially personalized) local models. Theoretically, we show that under some standard regularity assumptions, the proposed MARL-CAC algorithm requires $\mathcal{O}(ε^{-\frac{5}{2}})$ samples to achieve an $ε$-stationary solution (defined as the solution whose squared norm of the gradient of the objective function is less than $ε$). To the best of our knowledge, this work provides the first finite-sample guarantee for decentralized AC algorithm with partially personalized policies.

Shixiang Chen, Alfredo Garcia, Mingyi Hong et al.

We consider a distributed non-convex optimization where a network of agents aims at minimizing a global function over the Stiefel manifold. The global function is represented as a finite sum of smooth local functions, where each local function is associated with one agent and agents communicate with each other over an undirected connected graph. The problem is non-convex as local functions are possibly non-convex (but smooth) and the Steifel manifold is a non-convex set. We present a decentralized Riemannian stochastic gradient method (DRSGD) with the convergence rate of $\mathcal{O}(1/\sqrt{K})$ to a stationary point. To have exact convergence with constant stepsize, we also propose a decentralized Riemannian gradient tracking algorithm (DRGTA) with the convergence rate of $\mathcal{O}(1/K)$ to a stationary point. We use multi-step consensus to preserve the iteration in the local (consensus) region. DRGTA is the first decentralized algorithm with exact convergence for distributed optimization on Stiefel manifold.

Lingzhou Hong, Alfredo Garcia, Ceyhun Eksin

We consider a distributed estimation method in a setting with heterogeneous streams of correlated data distributed across nodes in a network. In the considered approach, linear models are estimated locally (i.e., with only local data) subject to a network regularization term that penalizes a local model that differs from neighboring models. We analyze computation dynamics (associated with stochastic gradient updates) and information exchange (associated with exchanging current models with neighboring nodes). We provide a finite-time characterization of convergence of the weighted ensemble average estimate and compare this result to federated learning, an alternative approach to estimation wherein a single model is updated by locally generated gradient updates. This comparison highlights the trade-off between speed vs precision: while model updates take place at a faster rate in federated learning, the proposed networked approach to estimation enables the identification of models with higher precision. We illustrate the method's general applicability in two examples: estimating a Markov random field using wireless sensor networks and modeling prey escape behavior of flocking birds based on a publicly available dataset.

Shi Pu, Alfredo Garcia

We study a distributed framework for stochastic optimization which is inspired by models of collective motion found in nature (e.g., swarming) with mild communication requirements. Specifically, we analyze a scheme in which each one of $N > 1$ independent threads, implements in a distributed and unsynchronized fashion, a stochastic gradient-descent algorithm which is perturbed by a swarming potential. Assuming the overhead caused by synchronization is not negligible, we show the swarming-based approach exhibits better performance than a centralized algorithm (based upon the average of $N$ observations) in terms of (real-time) convergence speed. We also derive an error bound that is monotone decreasing in network size and connectivity. We characterize the scheme's finite-time performances for both convex and non-convex objective functions.

Davood Hajinezhad, Mingyi Hong, Alfredo Garcia

In this paper, we consider distributed optimization problems over a multi-agent network, where each agent can only partially evaluate the objective function, and it is allowed to exchange messages with its immediate neighbors. Differently from all existing works on distributed optimization, our focus is given to optimizing a class of non-convex problems, and under the challenging setting where each agent can only access the zeroth-order information (i.e., the functional values) of its local functions. For different types of network topologies such as undirected connected networks or star networks, we develop efficient distributed algorithms and rigorously analyze their convergence and rate of convergence (to the set of stationary solutions). Numerical results are provided to demonstrate the efficiency of the proposed algorithms.