论文检索

Reinforcement Learning · Online

Zhengpeng Xie, Qiang Zhang, Fan Yang, Marco Hutter, Renjing Xu

Model-free reinforcement learning algorithms have seen remarkable progress, but key challenges remain. Trust Region Policy Optimization (TRPO) is known for ensuring monotonic policy improvement through conservative updates within a trust region, backed by strong theoretical guarantees. However, its reliance on complex second-order optimization limits its practical efficiency. Proximal Policy Optimization (PPO) addresses this by simplifying TRPO's approach using ratio clipping, improving efficiency but sacrificing some theoretical robustness. This raises a natural question: Can we combine the strengths of both methods? In this paper, we introduce Simple Policy Optimization (SPO), a novel unconstrained first-order algorithm. By slightly modifying the policy loss used in PPO, SPO can achieve the best of both worlds. Our new objective improves upon ratio clipping, offering stronger theoretical properties and better constraining the probability ratio within the trust region. Empirical results demonstrate that SPO outperforms PPO with a simple implementation, particularly for training large, complex network architectures end-to-end.

Optimization · Large Scale, Parallel and Distributed

Rustem Islamov, Yarden As, Ilyas Fatkhullin

Federated learning faces severe communication bottlenecks due to the high dimensionality of model updates. Communication compression with contractive compressors (e.g., Top-$K$) is often preferable in practice but can degrade performance without proper handling. Error feedback (EF) mitigates such issues but has been largely restricted for smooth, unconstrained problems, limiting its real-world applicability where non-smooth objectives and safety constraints are critical. We advance our understanding of EF in the canonical non-smooth convex setting by establishing new lower complexity bounds for first-order algorithms with contractive compression. Next, we propose Safe-EF, a novel algorithm that matches our lower bound (up to a constant) while enforcing safety constraints essential for practical applications. Extending our approach to the stochastic setting, we bridge the gap between theory and practical implementation. Extensive experiments in a reinforcement learning setup, simulating distributed humanoid robot training, validate the effectiveness of Safe-EF in ensuring safety and reducing communication complexity.

Deep Learning · Large Language Models

Yao Shu, Wenyang Hu, See-Kiong Ng, Bryan Kian Hsiang Low, Fei Yu

Large Language Models (LLMs) have become indispensable in numerous real-world applications. However, fine-tuning these models at scale, especially in federated settings where data privacy and communication efficiency are critical, presents significant challenges. Existing approaches often resort to parameter-efficient fine-tuning (PEFT) to mitigate communication overhead, but this typically comes at the cost of model accuracy. To this end, we propose *federated full-parameter tuning at scale for LLMs* (Ferret), **the first first-order method with shared randomness** to enable scalable full-parameter tuning of LLMs across decentralized data sources while maintaining competitive model accuracy. Ferret accomplishes this through three aspects: **(i)** it employs widely used first-order methods for efficient local updates; **(ii)** it projects these updates into a low-dimensional space to considerably reduce communication overhead; and **(iii)** it reconstructs local updates from this low-dimensional space with shared randomness to facilitate effective full-parameter global aggregation, ensuring fast convergence and competitive final performance. Our rigorous theoretical analyses and insights along with extensive experiments, show that Ferret significantly enhances the scalability of existing federated full-parameter tuning approaches by achieving high computational efficiency, reduced communication overhead, and fast convergence, all while maintaining competitive model accuracy. Our implementation is available at [https://github.com/allen4747/Ferret](https://github.com/allen4747/Ferret).

Optimization · Non-Convex

Jiaqi Leng, Bin Shi

With rapid advancements in machine learning, first-order algorithms have emerged as the backbone of modern optimization techniques, owing to their computational efficiency and low memory requirements. Recently, the connection between accelerated gradient methods and damped heavy-ball motion, particularly within the framework of Hamiltonian dynamics, has inspired the development of innovative quantum algorithms for continuous optimization. One such algorithm, Quantum Hamiltonian Descent (QHD), leverages quantum tunneling to escape saddle points and local minima, facilitating the discovery of global solutions in complex optimization landscapes. However, QHD faces several challenges, including slower convergence rates compared to classical gradient methods and limited robustness in highly non-convex problems due to the non-local nature of quantum states. Furthermore, the original QHD formulation primarily relies on function value information, which limits its effectiveness. Inspired by insights from high-resolution differential equations that have elucidated the acceleration mechanisms in classical methods, we propose an enhancement to QHD by incorporating gradient information, leading to what we call gradient-based QHD. This gradient-based QHD achieves faster convergence and significantly increases the likelihood of identifying global solutions. Numerical simulations on challenging problem instances demonstrate that this gradient-based QHD outperforms existing quantum and classical methods by at least an order of magnitude.

Applications · Computer Vision

Yinpeng Chen, Dongdong Chen, Xiyang Dai, Mengchen Liu, Yinan Feng, Youzuo Lin, Lu Yuan, Zicheng Liu

In this paper, we empirically demonstrate that natural images can be reconstructed with high fidelity from compressed representations using a simple first-order norm-plus-linear autoregressive (FINOLA) process—without relying on explicit positional information. Through systematic analysis, we observe that the learned coefficient matrices ($\mathbf{A}$ and $\mathbf{B}$) in FINOLA are typically invertible, and their product, $\mathbf{AB}^{-1}$, is diagonalizable across training runs. This structure enables a striking interpretation: FINOLA’s latent dynamics resemble a system of one-way wave equations evolving in a compressed latent space. Under this framework, each image corresponds to a unique solution of these equations. This offers a new perspective on image invariance, suggesting that the underlying structure of images may be governed by simple, invariant dynamic laws. Our findings shed light on a novel avenue for understanding and modeling visual data through the lens of latent-space dynamics and wave propagation.

Optimization · Stochastic

Zhenyu Sun, Ermin Wei

Unlike its vanilla counterpart with i.i.d. samples, stochastic optimization with Markovian sampling allows the sampling scheme following a Markov chain. This problem encompasses various applications that range from asynchronous distributed optimization to reinforcement learning. In this work, we lower bound the sample complexity of finding $\epsilon$-approximate critical solutions for any first-order methods when sampling is Markovian. We show that for samples drawn from stationary Markov processes with countable state space, any algorithm that accesses smooth, non-convex functions through queries to a stochastic gradient oracle, requires at least $\Omega(\epsilon^{-4})$ samples. Moreover, for finite Markov chains, we show a $\Omega(\epsilon^{-2})$ lower bound and propose a new algorithm, called MaC-SAGE, that is proven to (nearly) match our lower bound.

Deep Learning · Theory

Ruiqi Zhang, Jingfeng Wu, Peter Bartlett

We analyze the convergence of gradient descent (GD) with large, adaptive stepsizes for logistic regression on linearly separable data. The stepsize adapts to the current risk, scaled by a fixed base stepsize \eta. We prove that once the number of iterates t surpasses a margin-dependent threshold, the averaged GD iterate achieves a risk upper bound of \exp(-\Theta(\eta t)), where \eta can be chosen arbitrarily large. This implies that GD attains \emph{arbitrarily fast} convergence rates via large stepsizes, although the risk evolution might not be monotonic. In contrast, prior adaptive stepsize GD analyses require a monotonic risk decrease, limiting their rates to \exp(-\Theta(t)). We further establish a margin-dependent lower bound on the iteration complexity for any first-order method to attain a small risk, justifying the necessity of the burn-in phase in our analysis. Our results generalize to a broad class of loss functions and two-layer networks under additional assumptions.

Optimization

Lisha Chen, Quan Xiao, Ellen Fukuda, Xinyi Chen, Kun Yuan, Tianyi Chen

Multi-objective learning under user-specified preference is common in real-world problems such as multi-lingual speech recognition under fairness. In this work, we frame such a problem as a semivectorial bilevel optimization problem, whose goal is to optimize a pre-defined preference function, subject to the constraint that the model parameters are weakly Pareto optimal. To solve this problem, we convert the multi-objective constraints to a single-objective constraint through a merit function with an easy-to-evaluate gradient, and then, we use a penalty-based reformulation of the bilevel optimization problem. We theoretically establish the properties of the merit function, and the relations of solutions for the penalty reformulation and the constrained formulation. Then we propose algorithms to solve the reformulated single-level problem, and establish its convergence guarantees. We test the method on various synthetic and real-world problems. The results demonstrate the effectiveness of the proposed method in finding preference-guided optimal solutions to the multi-objective problem.

Deep Learning · Large Language Models

Jiawei Zhang, Xuan Yang, Taiqi Wang, Yu Yao, Aleksandr Petiushko, Bo Li

Traditional autonomous driving systems often struggle to connect high-level reasoning with low-level control, leading to suboptimal and sometimes unsafe behaviors. Recent advances in multimodal large language models (MLLMs), which process both visual and textual data, offer an opportunity to unify perception and reasoning. However, effectively embedding precise safety knowledge into MLLMs for autonomous driving remains a significant challenge.To address this, we propose SafeAuto, a framework that enhances MLLM-based autonomous driving by incorporating both unstructured and structured knowledge. First, we introduce a Position-Dependent Cross-Entropy (PDCE) loss to improve low-level control signal predictions when values are represented as text. Second, to explicitly integrate safety knowledge, we develop a reasoning component that translates traffic rules into first-order logic (e.g., "red light => stop") and embeds them into a probabilistic graphical model (e.g., Markov Logic Network) to verify predicted actions using recognized environmental attributes.Additionally, our Multimodal Retrieval-Augmented Generation (RAG) model leverages video, control signals, and environmental attributes to learn from past driving experiences. Integrating PDCE, MLN, and Multimodal RAG, SafeAuto outperforms existing baselines across multiple datasets, enabling more accurate, reliable, and safer autonomous driving. The code is available at https://github.com/AI-secure/SafeAuto.

Reinforcement Learning

Arman Sharifi Kolarijani, Tolga Ok, Peyman Mohajerin Esfahani, Mohamad Amin Sharifi Kolarijani

In this paper, we provide a novel algorithm for solving planning and learning problems of Markov decision processes. The proposed algorithm follows a policy iteration-type update by using a rank-one approximation of the transition probability matrix in the policy evaluation step. This rank-one approximation is closely related to the stationary distribution of the corresponding transition probability matrix, which is approximated using the power method. We provide theoretical guarantees for the convergence of the proposed algorithm to optimal (action-)value function with the same rate and computational complexity as the value iteration algorithm in the planning problem and as the Q-learning algorithm in the learning problem. Through our extensive numerical simulations, however, we show that the proposed algorithm consistently outperforms first-order algorithms and their accelerated versions for both planning and learning problems.

Theory · Optimization

Amit Attia, Ofir Gaash, Tomer Koren

We consider the problem of asynchronous stochastic optimization, where an optimization algorithm makes updates based on stale stochastic gradients of the objective that are subject to an arbitrary (possibly adversarial) sequence of delays. We present a procedure which, for any given $q \in (0,1]$, transforms any standard stochastic first-order method to an asynchronous method with convergence guarantee depending on the $q$-quantile delay of the sequence. This approach leads to convergence rates of the form $O(\tau_q/qT+\sigma/\sqrt{qT})$ for non-convex and $O(\tau_q^2/(q T)^2+\sigma/\sqrt{qT})$ for convex smooth problems, where $\tau_q$ is the $q$-quantile delay, generalizing and improving on existing results that depend on the average delay. We further show a method that automatically adapts to all quantiles simultaneously, without any prior knowledge of the delays, achieving convergence rates of the form $O(\inf_{q} \tau_q/qT+\sigma/\sqrt{qT})$ for non-convex and $O(\inf_{q} \tau_q^2/(q T)^2+\sigma/\sqrt{qT})$ for convex smooth problems. Our technique is based on asynchronous mini-batching with a careful batch-size selection and filtering of stale gradients.

Theory · Online Learning and Bandits

Rohan Deb, Mohammad Ghavamzadeh, Arindam Banerjee

Conservative Contextual Bandits (CCBs) address safety in sequential decision making by requiring that an agent's policy, along with minimizing regret, also satisfies a safety constraint: the performance is not worse than a baseline policy (e.g., the policy that the company has in production) by more than $(1+\alpha)$ factor. Prior work developed UCB-stylealgorithms for this problem in the multi-armed (Wu et al., 2016) and contextuallinear (Kazerouni et al., 2017) settings.However, in practice the cost of the armsis often a non-linear function, and therefore existing UCB algorithms are ineffective in such settings. In this paper, we consider CCBs beyond the linear case and develop two algorithms $\mathtt{C\text{-}SquareCB}$ and $\mathtt{C\text{-}FastCB}$, using Inverse Gap Weighting (IGW) based exploration and an online regression oracle. We show that the safety constraint is satisfied in high probability and that the regret for $\mathtt{C\text{-}SquareCB}$ is sub-linear in horizon $T$, while the the regret for $\mathtt{C\text{-}FastCB}$ is first-order and is sub-linear in $L^*$, the cumulative loss of the optimal policy. Subsequently, we use a neural network for function approximation and online gradient descent as the regression oracle to provide $\tilde{\mathcal{O}}\big(\sqrt{KT} + K/\alpha\big) $ and $\tilde{\mathcal{O}}\big(\sqrt{KL^*} + K (1 + 1/\alpha)\big)$ regret bounds respectively. Finally, we demonstrate the efficacy of our algorithms on real world data, and show that they significantly outperform the existing baseline while maintaining the performance guarantee.

Reinforcement Learning · Deep RL

Yinuo Wang, Wenxuan Wang, Xujie Song, Tong Liu, Yuming Yin, Liangfa Chen, Likun Wang, Jingliang Duan, Shengbo Li

The smoothness of control actions is a significant challenge faced by deep reinforcement learning (RL) techniques in solving optimal control problems. Existing RL-trained policies tend to produce non-smooth actions due to high-frequency input noise and unconstrained Lipschitz constants in neural networks. This article presents a Smooth ODE (SmODE) network capable of simultaneously addressing both causes of unsmooth control actions, thereby enhancing policy performance and robustness under noise condition. We first design a smooth ODE neuron with first-order low-pass filtering expression, which can dynamically filter out high frequency noises of hidden state by a learnable state-based system time constant. Additionally, we construct a state-based mapping function, $g$, and theoretically demonstrate its capacity to control the ODE neuron's Lipschitz constant. Then, based on the above neuronal structure design, we further advanced the SmODE network serving as RL policy approximators. This network is compatible with most existing RL algorithms, offering improved adaptability compared to prior approaches. Various experiments show that our SmODE network demonstrates superior anti-interference capabilities and smoother action outputs than the multi-layer perception and smooth network architectures like LipsNet.

Theory · Optimization

Siqi Zhang, Yifan Hu

In this blog, we summarize the upper and lower complexity bounds of first-order algorithms in minimization and minimax optimization problems. Within the classical oracle model framework, we review the state-of-the-art upper and lower bound results in various settings, aiming to identify gaps in existing research. With the rapid development of applications like machine learning and operation research, we further identify some recent works that revised the classical settings of optimization algorithms study.

Miscellaneous Aspects of Machine Learning · Representation Learning

Yichao Liang, Nishanth Kumar, Hao Tang, Adrian Weller, Joshua B Tenenbaum, Tom Silver, Joao F. Henriques, Kevin Ellis

Broadly intelligent agents should form task-specific abstractions that selectively expose the essential elements of a task, while abstracting away the complexity of the raw sensorimotor space. In this work, we present Neuro-Symbolic Predicates, a first-order abstraction language that combines the strengths of symbolic and neural knowledge representations. We outline an online algorithm for inventing such predicates and learning abstract world models. We compare our approach to hierarchical reinforcement learning, vision-language model planning, and symbolic predicate invention approaches, on both in- and out-of-distribution tasks across five simulated robotic domains. Results show that our approach offers better sample complexity, stronger out-of-distribution generalization, and improved interpretability.

Optimization · Non-Convex

Weiyuan Gong, Chenyi Zhang, Tongyang Li

In this paper, we systematically study quantum algorithms for finding an $\epsilon$-approximate second-order stationary point ($\epsilon$-SOSP) of a $d$-dimensional nonconvex function, a fundamental problem in nonconvex optimization, with noisy zeroth- or first-order oracles as inputs. We first prove that, up to noise of $O(\epsilon^{10}/d^5)$, perturbed accelerated gradient descent equipped with quantum gradient estimation takes $O(\log d/\epsilon^{1.75})$ quantum queries to find an $\epsilon$-SOSP. We then prove that standard perturbed gradient descent is robust to the noise of $O(\epsilon^6/d^4)$ and $O(\epsilon/d^{0.5+\zeta})$ for any $\zeta>0$ on the zeroth- and first-order oracles, respectively, which provides a quantum algorithm with poly-logarithmic query complexity. Furthermore, we propose a stochastic gradient descent algorithm using quantum mean estimation on the Gaussian smoothing of noisy oracles, which is robust to $O(\epsilon^{1.5}/d)$ and $O(\epsilon/\sqrt{d})$ noise on the zeroth- and first-order oracles, respectively. The quantum algorithm takes $O(d^{2.5}/\epsilon^{3.5})$ and $O(d^2/\epsilon^3)$ queries to the two oracles, giving a polynomial speedup over the classical counterparts. As a complement, we characterize the domains where quantum algorithms can find an $\epsilon$-SOSP with poly-logarithmic, polynomial, or exponential number of queries in $d$, or the problem is information-theoretically unsolvable even with an infinite number of queries. In addition, we prove an $\Omega(\epsilon^{-12/7})$ lower bound on $\epsilon$ for any randomized classical and quantum algorithm to find an $\epsilon$-SOSP using either noisy zeroth- or first-order oracles.

Deep Learning · Generative Models and Autoencoders

Guangyi Wang, Yuren Cai, lijiang Li, Wei Peng, Song-Zhi Su

Diffusion Probabilistic Models (DPMs) have shown remarkable potential in image generation, but their sampling efficiency is hindered by the need for numerous denoising steps. Most existing solutions accelerate the sampling process by proposing fast ODE solvers. However, the inevitable discretization errors of the ODE solvers are significantly magnified when the number of function evaluations (NFE) is fewer. In this work, we propose PFDiff, a novel training-free and orthogonal timestep-skipping strategy, which enables existing fast ODE solvers to operate with fewer NFE. Specifically, PFDiff initially utilizes score replacement from past time steps to predict a springboard. Subsequently, it employs this ``springboard" along with foresight updates inspired by Nesterov momentum to rapidly update current intermediate states. This approach effectively reduces unnecessary NFE while correcting for discretization errors inherent in first-order ODE solvers. Experimental results demonstrate that PFDiff exhibits flexible applicability across various pre-trained DPMs, particularly excelling in conditional DPMs and surpassing previous state-of-the-art training-free methods. For instance, using DDIM as a baseline, we achieved 16.46 FID (4 NFE) compared to 138.81 FID with DDIM on ImageNet 64x64 with classifier guidance, and 13.06 FID (10 NFE) on Stable Diffusion with 7.5 guidance scale. Code is available at https://github.com/onefly123/PFDiff.

Optimization · Zero-order and Black-box Optimization

Yiming Chen, Yuan Zhang, Liyuan Cao, Kun Yuan, Zaiwen Wen

Parameter-efficient fine-tuning (PEFT) significantly reduces memory costs when adapting large language models (LLMs) for downstream applications. However, traditional first-order (FO) fine-tuning algorithms incur substantial memory overhead due to the need to store activation values for back-propagation during gradient computation, particularly in long-context fine-tuning tasks. Zeroth-order (ZO) algorithms offer a promising alternative by approximating gradients using finite differences of function values, thus eliminating the need for activation storage. Nevertheless, existing ZO methods struggle to capture the low-rank gradient structure common in LLM fine-tuning, leading to suboptimal performance. This paper proposes a low-rank ZO gradient estimator and introduces a novel **lo**w-rank **ZO** algorithm (LOZO) that effectively captures this structure in LLMs. We provide convergence guarantees for LOZO by framing it as a subspace optimization method. Additionally, its low-rank nature enables LOZO to integrate with momentum techniques while incurring negligible extra memory costs. Extensive experiments across various model sizes and downstream tasks demonstrate that LOZO and its momentum-based variant outperform existing ZO methods and closely approach the performance of FO algorithms.

Daogao Liu, Kunal Talwar

There is a gap between finding a first-order stationary point (FOSP) and a second-order stationary point (SOSP) under differential privacy constraints, and it remains unclear whether privately finding an SOSP is more challenging than finding an FOSP. Specifically, Ganesh et al. (2023) claimed that an $\alpha$-SOSP can be found with $\alpha=\Tilde{O}(\frac{1}{n^{1/3}}+(\frac{\sqrt{d}}{n\epsilon})^{3/7})$, where $n$ is the dataset size, $d$ is the dimension, and $\epsilon$ is the differential privacy parameter.However, a recent analysis revealed an issue in their saddle point escape procedure, leading to weaker guarantees. Building on the SpiderBoost algorithm framework, we propose a new approach that uses adaptive batch sizes and incorporates the binary tree mechanism.Our method not only corrects this issue but also improves the results for privately finding an SOSP, achieving $\alpha=\Tilde{O}(\frac{1}{n^{1/3}}+(\frac{\sqrt{d}}{n\epsilon})^{1/2})$. This improved bound matches the state-of-the-art for finding a FOSP, suggesting that privately finding an SOSP may be achievable at no additional cost.

Optimization · Non-Convex

Frank Zhengqing Wu, Berfin Simsek, François Ged

In this paper, we study the loss landscape of one-hidden-layer neural networks with ReLU-like activation functions trained with the empirical squared loss using gradient descent (GD). We identify the stationary points of such networks, which significantly slow down loss decrease during training. To capture such points while accounting for the non-differentiability of the loss, the stationary points that we study are directional stationary points, rather than other notions like Clarke stationary points. We show that, if a stationary point does not contain "escape neurons", which are defined with first-order conditions, it must be a local minimum. Moreover, for the scalar-output case, the presence of an escape neuron guarantees that the stationary point is not a local minimum. Our results refine the description of the *saddle-to-saddle* training process starting from infinitesimally small (vanishing) initialization for shallow ReLU-like networks: By precluding the saddle escape types that previous works did not rule out, we advance one step closer to a complete picture of the entire dynamics. Moreover, we are also able to fully discuss how network embedding, which is to instantiate a narrower network with a wider network, reshapes the stationary points.