Robust Markov Decision Processes (RMDPs) have recently been recognized as a valuable and promising approach to discovering a policy with creditable performance, particularly in the presence of a dynamic environment and estimation errors in the transition matrix due to limited data. Despite extensive exploration of dynamic programming algorithms for solving RMDPs, there has been a notable upswing in interest in developing efficient algorithms using the policy gradient method. In this paper, we propose the first single-loop robust policy gradient (SRPG) method with the global optimality guarantee for solving RMDPs through its minimax formulation. Moreover, we complement the convergence analysis of the nonconvex-nonconcave min-max optimization problem with the objective function's gradient dominance property, which is not explored in the prior literature. Numerical experiments validate the efficacy of SRPG, demonstrating its faster and more robust convergence behavior compared to its nested-loop counterpart.
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Reinforcement Learning · Batch/Offline
In offline reinforcement learning (RL), the performance of the learned policy highly depends on the quality of offline datasets. However, the offline dataset contains very limited optimal trajectories in many cases. This poses a challenge for offline RL algorithms, as agents must acquire the ability to transit to high-reward regions. To address this issue, we introduce Diffusionbased Trajectory Stitching (DiffStitch), a novel diffusion-based data augmentation pipeline that systematically generates stitching transitions between trajectories. DiffStitch effectively connects low-reward trajectories with high-reward trajectories, forming globally optimal trajectories and thereby mitigating the challenges faced by offline RL algorithms in learning trajectory stitching. Empirical experiments conducted on D4RL datasets demonstrate the effectiveness of our pipeline across RL methodologies. Notably, DiffStitch demonstrates substantial enhancements in the performance of one-step methods(IQL), imitation learning methods(TD3+BC) and trajectory optimization methods(DT). Our code is publicly available at https://github.com/guangheli12/DiffStitch
Miscellaneous Aspects of Machine Learning · Representation Learning
We study deep neural networks for the multi-label classification (MLab) task through the lens of neural collapse (NC). Previous works have been restricted to the multi-class classification setting and discovered a prevalent NC phenomenon comprising of the following properties for the last-layer features: (i) the variability of features within every class collapses to zero, (ii) the set of feature means form an equi-angular tight frame (ETF), and (iii) the last layer classifiers collapse to the feature mean upon some scaling. We generalize the study to multi-label learning, and prove for the first time that a generalized NC phenomenon holds with the "pick-all-label'' formulation, which we term as MLab NC. While the ETF geometry remains consistent for features with a single label, multi-label scenarios introduce a unique combinatorial aspect we term the "tag-wise average" property, where the means of features with multiple labels are the scaled averages of means for single-label instances. Theoretically, under proper assumptions on the features, we establish that the only global optimizer of the pick-all-label cross-entropy loss satisfy the multi-label NC. In practice, we demonstrate that our findings can lead to better test performance with more efficient training techniques for MLab learning.
In this paper, we present DetKDS, the first framework that searches for optimal detection distillation policies. Manual design of detection distillers becomes challenging and time-consuming due to significant disparities in distillation behaviors between detectors with different backbones, paradigms, and label assignments. To tackle these challenges, we leverage search algorithms to discover optimal distillers for homogeneous and heterogeneous student-teacher pairs. Firstly, our search space encompasses global features, foreground-background features, instance features, logits response, and localization response as inputs. Then, we construct omni-directional cascaded transformations and obtain the distiller by selecting the advanced distance function and common weight value options. Finally, we present a divide-and-conquer evolutionary algorithm to handle the explosion of the search space. In this strategy, we first evolve the best distiller formulations of individual knowledge inputs and then optimize the combined weights of these multiple distillation losses. DetKDS automates the distillation process without requiring expert design or additional tuning, effectively reducing the teacher-student gap in various scenarios. Based on the analysis of our search results, we provide valuable guidance that contributes to detection distillation designs. Comprehensive experiments on different detectors demonstrate that DetKDS outperforms state-of-the-art methods in detection and instance segmentation tasks. For instance, DetKDS achieves significant gains than baseline detectors: $+3.7$, $+4.1$, $+4.0$, $+3.7$, and $+3.5$ AP on RetinaNet, Faster-RCNN, FCOS, RepPoints, and GFL, respectively. Code at: https://github.com/lliai/DetKDS.
Optimization · Non-Convex
Supervised matrix factorization (SMF) is a classical machine learning method that seeks low-dimensional feature extraction and classification tasks at the same time. Training an SMF model involves solving a non-convex and factor-wise constrained optimization problem with at least three blocks of parameters. Due to the high non-convexity and constraints, theoretical understanding of the optimization landscape of SMF has been limited. In this paper, we provide an extensive local landscape analysis for SMF and derive several theoretical and practical applications. Analyzing diagonal blocks of the Hessian naturally leads to a block coordinate descent (BCD) algorithm with adaptive step sizes. We provide global convergence and iteration complexity guarantees for this algorithm. Full Hessian analysis gives minimum $L_{2}$-regularization to guarantee local strong convexity and robustness of parameters. We establish a local estimation guarantee under a statistical SMF model. We also propose a novel GPU-friendly neural implementation of the BCD algorithm and validate our theoretical findings through numerical experiments. Our work contributes to a deeper understanding of SMF optimization, offering insights into the optimization landscape and providing practical solutions to enhance its performance.
Theory · Optimization
The Gradient Descent-Ascent (GDA) algorithm, designed to solve minimax optimization problems, takes the descent and ascent steps either simultaneously (Sim-GDA) or alternately (Alt-GDA). While Alt-GDA is commonly observed to converge faster, the performance gap between the two is not yet well understood theoretically, especially in terms of global convergence rates. To address this theory-practice gap, we present fine-grained convergence analyses of both algorithms for strongly-convex-strongly-concave and Lipschitz-gradient objectives. Our new iteration complexity upper bound of Alt-GDA is strictly smaller than the lower bound of Sim-GDA; i.e., Alt-GDA is provably faster. Moreover, we propose Alternating-Extrapolation GDA (Alex-GDA), a general algorithmic framework that subsumes Sim-GDA and Alt-GDA, for which the main idea is to alternately take gradients from extrapolations of the iterates. We show that Alex-GDA satisfies a smaller iteration complexity bound, identical to that of the Extra-gradient method, while requiring less gradient computations. We also prove that Alex-GDA enjoys linear convergence for bilinear problems, for which both Sim-GDA and Alt-GDA fail to converge at all.
Deep Learning · Theory
In this paper, we study the optimality gap between two-layer ReLU networks regularized with weight decay and their convex relaxations. We show that when the training data is random, the relative optimality gap between the original problem and its relaxation can be bounded by a factor of O(√log n), where n is the number of training samples. A simple application leads to a tractable polynomial-time algorithm that is guaranteed to solve the original non-convex problem up to a logarithmic factor. Moreover, under mild assumptions, we show that local gradient methods converge to a point with low training loss with high probability. Our result is an exponential improvement compared to existing results and sheds new light on understanding why local gradient methods work well.
Optimization · Discrete and Combinatorial Optimization
Since graph neural networks (GNNs) are often vulnerable to attack, we need to know when we can trust them. We develop a computationally effective approach towards providing robust certificates for message-passing neural networks (MPNNs) using a Rectified Linear Unit (ReLU) activation function. Because our work builds on mixed-integer optimization, it encodes a wide variety of subproblems, for example it admits (i) both adding and removing edges, (ii) both global and local budgets, and (iii) both topological perturbations and feature modifications. Our key technology, topology-based bounds tightening, uses graph structure to tighten bounds. We also experiment with aggressive bounds tightening to dynamically change the optimization constraints by tightening variable bounds. To demonstrate the effectiveness of these strategies, we implement an extension to the open-source branch-and-cut solver SCIP. We test on both node and graph classification problems and consider topological attacks that both add and remove edges.
Deep Learning · Large Language Models
State-of-the-art language models can exhibit reasoning refinement capabilities on math, science or coding tasks. However, recent work demonstrates that even the best models struggle to identify *when and where to refine* without access to external feedback. In this paper, we propose Stepwise ORMs (**SORMs**) which are trained, only on synthetic data, to approximate the expected future reward of the optimal policy or $V^{\star}$ as a form of Process-based reward modeling. Our experiments show that SORMs can more accurately detect incorrect reasoning steps compared to ORMs, thus enabling them to give precise step-level feedback to refinement models. We then train *global* refinement models, which take only the question and a draft solution as input and predict a corrected solution, and *local* refinement models which also take as input a critique indicating the location of the first reasoning error. We generate training data for both models synthetically by reusing data used to train the SORM. We find combining global and local refinements, using the ORM as a reranker, significantly outperforms either one individually, as well as a best of three sample baseline. With this strategy we can improve the accuracy of a LLaMA-2 13B model (already fine-tuned with RL) on GSM8K from 53% to 65% when greedily sampled.
Theory · Online Learning and Bandits
In traditional federated learning, a single global model cannot perform equally well for all clients. Therefore, the need to achieve the *client-level fairness* in federated system has been emphasized, which can be realized by modifying the static aggregation scheme for updating the global model to an adaptive one, in response to the local signals of the participating clients. Our work reveals that existing fairness-aware aggregation strategies can be unified into an online convex optimization framework, in other words, a central server's *sequential decision making* process. To enhance the decision making capability, we propose simple and intuitive improvements for suboptimal designs within existing methods, presenting $\texttt{AAggFF}$. Considering practical requirements, we further subdivide our method tailored for the *cross-device* and the *cross-silo* settings, respectively. Theoretical analyses guarantee sublinear regret upper bounds for both settings: $\mathcal{O}(\sqrt{T \log{K}})$ for the cross-device setting, and $\mathcal{O}(K \log{T})$ for the cross-silo setting, with $K$ clients and $T$ federation rounds. Extensive experiments demonstrate that the federated system equipped with $\texttt{AAggFF}$ achieves better degree of client-level fairness than existing methods in both practical settings.
FedRC: Tackling Diverse Distribution Shifts Challenge in Federated Learning by Robust Clustering
PDF ↗Deep Learning · Algorithms
Federated Learning (FL) is a machine learning paradigm that safeguards privacy by retaining client data on edge devices. However, optimizing FL in practice can be challenging due to the diverse and heterogeneous nature of the learning system. Though recent research has focused on improving the optimization of FL when distribution shifts occur among clients, ensuring global performance when multiple types of distribution shifts occur simultaneously among clients---such as feature distribution shift, label distribution shift, and concept shift---remain under-explored. In this paper, we identify the learning challenges posed by the simultaneous occurrence of diverse distribution shifts and propose a clustering principle to overcome these challenges. Through our research, we find that existing methods fail to address the clustering principle. Therefore, we propose a novel clustering algorithm framework, dubbed as FedRC, which adheres to our proposed clustering principle by incorporating a bi-level optimization problem and a novel objective function. Extensive experiments demonstrate that FedRC significantly outperforms other SOTA cluster-based FL methods. Our code will be publicly available.
Applications · Everything Else
Macro placement is a crucial step in modern chip design, and reinforcement learning (RL) has recently emerged as a promising technique for improving the placement quality. However, existing RL-based techniques are hindered by their low sample efficiency, requiring numerous online rollouts or substantial offline expert data to achieve bootstrap, which are often impractical in industrial scenarios. To address this challenge, we propose a novel sample-efficient framework, namely **EfficientPlace**, for fast macro placement. EfficientPlace integrates a global tree search algorithm to strategically direct the optimization process, as well as a RL agent for local policy learning to advance the tree search. Experiments on commonly used benchmarks demonstrate that EfficientPlace achieves remarkable placement quality within a short timeframe, outperforming recent state-of-the-art approaches.
Optimization · Non-Convex
In this paper we theoretically show that interior-point methods based on self-concordant barriers possess favorable global complexity beyond their standard application area of convex optimization. To do that we propose first- and second-order methods for non-convex optimization problems with general convex set constraints and linear constraints. Our methods attain a suitably defined class of approximate first- or second-order KKT points with the worst-case iteration complexity similar to unconstrained problems, namely $O(\varepsilon^{-2})$ (first-order) and $O(\varepsilon^{-3/2})$ (second-order), respectively.
Global Reinforcement Learning : Beyond Linear and Convex Rewards via Submodular Semi-gradient Methods
PDF ↗Reinforcement Learning
In classic Reinforcement Learning (RL), the agent maximizes an additive objective of the visited states, e.g., a value function. Unfortunately, objectives of this type cannot model many real-world applications such as experiment design, exploration, imitation learning, and risk-averse RL to name a few. This is due to the fact that additive objectives disregard interactions between states that are crucial for certain tasks. To tackle this problem, we introduce *Global* RL (GRL), where rewards are *globally* defined over trajectories instead of *locally* over states. Global rewards can capture *negative interactions* among states, e.g., in exploration, via submodularity, *positive interactions*, e.g., synergetic effects, via supermodularity, while mixed interactions via combinations of them. By exploiting ideas from submodular optimization, we propose a novel algorithmic scheme that converts any GRL problem to a sequence of classic RL problems and solves it efficiently with curvature-dependent approximation guarantees. We also provide hardness of approximation results and empirically demonstrate the effectiveness of our method on several GRL instances.
Reinforcement Learning · Policy Search
Robust Markov decision process (robust MDP) is an important machine learning framework to make a reliable policy that is robust to environmental perturbation. Despite empirical success and popularity of policy gradient methods, existing policy gradient methods require at least iteration complexity $\mathcal{O}(\epsilon^{-4})$ to converge to the global optimal solution of s-rectangular robust MDPs with $\epsilon$-accuracy and are limited to deterministic setting with access to exact gradients and small state space that are impractical in many applications. In this work, we propose an accelerated policy gradient algorithm with iteration complexity $\mathcal{O}(\epsilon^{-3}\ln\epsilon^{-1})$ in the deterministic setting using entropy regularization. Furthermore, we extend this algorithm to stochastic setting with access to only stochastic gradients and large state space which achieves the sample complexity $\mathcal{O}(\epsilon^{-7}\ln\epsilon^{-1})$. In the meantime, our algorithms are also the first scalable policy gradient methods to entropy-regularized robust MDPs, which provide an important but underexplored machine learning framework.
Deep Learning · Large Language Models
Harnessing the power of human-annotated data through Supervised Fine-Tuning (SFT) is pivotal for advancing Large Language Models (LLMs). In this paper, we delve into the prospect of growing a strong LLM out of a weak one without the need for acquiring additional human-annotated data. We propose a new fine-tuning method called Self-Play fIne-tuNing (SPIN), which starts from a supervised fine-tuned model. At the heart of SPIN lies a self-play mechanism, where the LLM refines its capability by playing against instances of itself. More specifically, the LLM generates its own training data from its previous iterations, refining its policy by discerning these self-generated responses from those obtained from human-annotated data. Our method progressively elevates the LLM from a nascent model to a formidable one, unlocking the full potential of human-annotated demonstration data for SFT. Theoretically, we prove that the global optimum to the training objective function of our method is achieved only when the LLM policy aligns with the target data distribution. Empirically, we evaluate our method on several benchmark datasets including the HuggingFace Open LLM Leaderboard, MT-Bench, and datasets from Big-Bench. Our results show that SPIN can significantly improve the LLM's performance across a variety of benchmarks and even outperform models trained through direct preference optimization (DPO) supplemented with extra GPT-4 preference data. This sheds light on the promise of self-play, enabling the achievement of human-level performance in LLMs without the need for expert opponents.
An Online Optimization Perspective on First-Order and Zero-Order Decentralized Nonsmooth Nonconvex Stochastic Optimization
PDF ↗Optimization · Non-Convex
We investigate the finite-time analysis of finding ($\delta, \epsilon$)-stationary points for nonsmooth nonconvex objectives in decentralized stochastic optimization. A set of agents aim at minimizing a global function using only their local information by interacting over a network. We present a novel algorithm, called Multi Epoch Decentralized Online Learning (ME-DOL), for which we establish the sample complexity in various settings. First, using a recently proposed online-to-nonconvex technique, we show that our algorithm recovers the optimal convergence rate of smooth nonconvex objectives. We then extend our analysis to the nonsmooth setting, building on properties of randomized smoothing and Goldstein-subdifferential sets. We establish the sample complexity of $O(\delta^{-1}\epsilon^{-3})$, which to the best of our knowledge is the first finite-time guarantee for decentralized nonsmooth nonconvex stochastic optimization in the first-order setting (without weak-convexity), matching its optimal centralized counterpart. We further prove the same rate for the zero-order oracle setting without using variance reduction.
Mean Field Langevin Actor-Critic: Faster Convergence and Global Optimality beyond Lazy Learning
PDF ↗Theory · Reinforcement Learning and Planning
This work explores the feature learning capabilities of deep reinforcement learning algorithms in the pursuit of optimal policy determination. We particularly examine an over-parameterized neural actor-critic framework within the mean-field regime, where both actor and critic components undergo updates via policy gradient and temporal-difference (TD) learning, respectively. We introduce the *mean-field Langevin TD learning* (MFLTD) method, enhancing mean-field Langevin dynamics with proximal TD updates for critic policy evaluation, and assess its performance against conventional approaches through numerical analysis. Additionally, for actor policy updates, we present the *mean-field Langevin policy gradient* (MFLPG), employing policy gradient techniques augmented by Wasserstein gradient flows for parameter space exploration. Our findings demonstrate that MFLTD accurately identifies the true value function, while MFLPG ensures linear convergence of actor sequences towards the globally optimal policy, considering a Kullback-Leibler divergence regularized framework. Through both time particle and discretized analysis, we substantiate the linear convergence guarantees of our neural actor-critic algorithms, representing a notable contribution to neural reinforcement learning focusing on *global optimality* and *feature learning*, extending the existing understanding beyond the conventional scope of lazy training.
Closing the Gap: Achieving Global Convergence (Last Iterate) of Actor-Critic under Markovian Sampling with Neural Network Parametrization
PDF ↗Reinforcement Learning · Deep RL
The current state-of-the-art theoretical analysis of Actor-Critic (AC) algorithms significantly lags in addressing the practical aspects of AC implementations. This crucial gap needs bridging to bring the analysis in line with practical implementations of AC. To address this, we advocate for considering the MMCLG criteria: **M**ulti-layer neural network parametrization for actor/critic, **M**arkovian sampling, **C**ontinuous state-action spaces, the performance of the **L**ast iterate, and **G**lobal optimality. These aspects are practically significant and have been largely overlooked in existing theoretical analyses of AC algorithms. In this work, we address these gaps by providing the first comprehensive theoretical analysis of AC algorithms that encompasses all five crucial practical aspects (covers MMCLG criteria). We establish global convergence sample complexity bounds of $\tilde{\mathcal{O}}\left( \epsilon^{-3} \right)$. We achieve this result through our novel use of the weak gradient domination property of MDP's and our unique analysis of the error in critic estimation.
Reinforcement Learning
In this paper, we propose a policy gradient method for confounded partially observable Markov decision processes (POMDPs) with continuous state and observation spaces in the offline setting. We first establish a novel identification result to non-parametrically estimate any history-dependent policy gradient under POMDPs using the offline data. The identification enables us to solve a sequence of conditional moment restrictions and adopt the min-max learning procedure with general function approximation for estimating the policy gradient. We then provide a finite-sample non-asymptotic bound for estimating the gradient uniformly over a pre-specified policy class in terms of the sample size, length of horizon, concentratability coefficient and the measure of ill-posedness in solving the conditional moment restrictions. Lastly, by deploying the proposed gradient estimation in the gradient ascent algorithm, we show the global convergence of the proposed algorithm in finding the history-dependent optimal policy under some technical conditions. To the best of our knowledge, this is the first work studying the policy gradient method for POMDPs under the offline setting.