Gradient descent is slow to converge for ill-conditioned problems and non-convex problems. An important technique for acceleration is step-size adaptation. The first part of this paper contains a detailed review of step-size adaptation methods, including Polyak step-size, L4, LossGrad, Adam, IDBD, and Hypergradient descent, and the relation of step-size adaptation to meta-gradient methods. In the second part of this paper, we propose a new class of methods of accelerating gradient descent that have some distinctiveness from existing techniques. The new methods, which we call {\em step-size planning}, use the {\em update experience} to learn an improved way of updating the parameters. The methods organize the experience into $K$ steps away from each other to facilitate planning. From the past experience, our planning algorithm, Csawg, learns a step-size model which is a form of multi-step machine that predicts future updates. We extends Csawg to applying step-size planning multiple steps, which leads to further speedup. We discuss and highlight the projection power of the diagonal-matrix step-size for future large scale applications. We show for a convex problem, our methods can surpass the convergence rate of Nesterov's accelerated gradient, $1 - \sqrt{μ/L}$, where $μ, L$ are the strongly convex factor of the loss function $F$ and the Lipschitz constant of $F'$, which is the theoretical limit for the convergence rate of first-order methods. On the well-known non-convex Rosenbrock function, our planning methods achieve zero error below 500 gradient evaluations, while gradient descent takes about 10000 gradient evaluations to reach a $10^{-3}$ accuracy. We discuss the connection of step-size planing to planning in reinforcement learning, in particular, Dyna architectures.
(This is a shorter abstract than in the paper because of length requirement)
With the impact of real-time processing being realized in the recent past, the need for efficient implementations of reinforcement learning algorithms has been on the rise. Albeit the numerous advantages of Bellman equations utilized in RL algorithms, they are not without the large search space of design parameters. This research aims to shed light on the design space exploration associated with reinforcement learning parameters, specifically that of Policy Iteration. Given the large computational expenses of fine-tuning the parameters of reinforcement learning algorithms, we propose an auto-t…
Indian Institute of Science Bangalore（班加罗尔印度科学研究所）
Autonomous marine vehicles play an essential role in many ocean science and engineering applications. Planning time and energy optimal paths for these vehicles to navigate in stochastic dynamic ocean environments is essential to reduce operational costs. In some missions, they must also harvest solar, wind, or wave energy (modeled as a stochastic scalar field) and move in optimal paths that minimize net energy consumption. Markov Decision Processes (MDPs) provide a natural framework for sequential decision-making for robotic agents in such environments. However, building a realistic model and …
Beyond the Next Step: Variable-Length Latent World Models for Long-Horizon Planning
State Key Lab of General Artificial Intelligence, School of Intelligence Science and Technology, Peking University（北京大学智能科学与技术学院通用人工智能国家重点实验室）；Amazon AGI SF Lab（亚马逊AGI旧金山实验室）；Institute for Artificial Intelligence, Peking University（北京大学人工智能研究院）
Linear temporal logic and automaton-based run-time verification provide a powerful framework for designing task and motion planning algorithms for autonomous agents. The drawback to this approach is the computational cost of operating on high resolution discrete abstractions of continuous dynamical systems. In particular, the computational bottleneck that arises is converting perceived environment variables into a labeling function on the states of a Kripke structure or analogously the transitions of a labeled transition system. This paper presents the design and empirical evaluation of an app…
Tel Aviv University（特拉维夫大学）；Google Research（谷歌研究院）
We study the algorithmic stability of Nesterov's accelerated gradient method. For convex quadratic objectives, Chen et al. (2018) proved that the uniform stability of the method grows quadratically with the number of optimization steps, and conjectured that the same is true for the general convex and smooth case. We disprove this conjecture and show, for two notions of algorithmic stability (including uniform stability), that the stability of Nesterov's accelerated method in fact deteriorates exponentially fast with the number of gradient steps. This stands in sharp contrast to the bounds in t…
General AI Lab（通用人工智能实验室）；Horizon Robotics Inc.（地平线机器人技术有限公司）
Standard model-free reinforcement learning algorithms optimize a policy that generates the action to be taken in the current time step in order to maximize expected future return. While flexible, it faces difficulties arising from the inefficient exploration due to its single step nature. In this work, we present Generative Planning method (GPM), which can generate actions not only for the current step, but also for a number of future steps (thus termed as generative planning). This brings several benefits to GPM. Firstly, since GPM is trained by maximizing value, the plans generated from it c…
We study gradient descent (GD) with a constant stepsize for $\ell_2$-regularized logistic regression with linearly separable data. Classical theory suggests small stepsizes to ensure monotonic reduction of the optimization objective, achieving exponential convergence in $\widetilde{\mathcal{O}}(κ)$ steps with $κ$ being the condition number. Surprisingly, we show that this can be accelerated to $\widetilde{\mathcal{O}}(\sqrtκ)$ by simply using a large stepsize -- for which the objective evolves nonmonotonically. The acceleration brought by large stepsizes extends to minimizing the population ri…
Facebook AI Research（脸书人工智能研究院）；Microsoft Research（微软研究院）；Technion（以色列理工学院）；Google Research（谷歌研究院）；Nvidia Research（英伟达研究院）
Real Time Dynamic Programming (RTDP) is an online algorithm based on Dynamic Programming (DP) that acts by 1-step greedy planning. Unlike DP, RTDP does not require access to the entire state space, i.e., it explicitly handles the exploration. This fact makes RTDP particularly appealing when the state space is large and it is not possible to update all states simultaneously. In this we devise a multi-step greedy RTDP algorithm, which we call $h$-RTDP, that replaces the 1-step greedy policy with a $h$-step lookahead policy. We analyze $h$-RTDP in its exact form and establish that increasing the …
University of Toronto（多伦多大学）；Vector Institute（向量研究所）；MIT（麻省理工学院）；Toyota Technological Institute at Chicago（芝加哥丰田技术研究所）
Planning - the ability to analyze the structure of a problem in the large and decompose it into interrelated subproblems - is a hallmark of human intelligence. While deep reinforcement learning (RL) has shown great promise for solving relatively straightforward control tasks, it remains an open problem how to best incorporate planning into existing deep RL paradigms to handle increasingly complex environments. One prominent framework, Model-Based RL, learns a world model and plans using step-by-step virtual rollouts. This type of world model quickly diverges from reality when the planning hori…
Maynooth University（梅努斯大学）；Max-Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）
We consider gradient descent with `momentum', a widely used method for loss function minimization in machine learning. This method is often used with `Nesterov acceleration', meaning that the gradient is evaluated not at the current position in parameter space, but at the estimated position after one step. In this work, we show that the algorithm can be improved by extending this `acceleration' --- by using the gradient at an estimated position several steps ahead rather than just one step ahead. How far one looks ahead in this `super-acceleration' algorithm is determined by a new hyperparamet…
Grupo Oesía（奥西亚集团）；Universitat Pompeu Fabra（庞培法布拉大学）
Optimal action selection in decision problems characterized by sparse, delayed rewards is still an open challenge. For these problems, current deep reinforcement learning methods require enormous amounts of data to learn controllers that reach human-level performance. In this work, we propose a method that interleaves planning and learning to address this issue. The planning step hinges on the Iterated-Width (IW) planner, a state of the art planner that makes explicit use of the state representation to perform structured exploration. IW is able to scale up to problems independently of the size…
University of Massachusetts（马萨诸塞大学）；Mississippi State University（密西西比州立大学）
Symbolic representations have been used successfully in off-line planning algorithms for Markov decision processes. We show that they can also improve the performance of on-line planners. In addition to reducing computation time, symbolic generalization can reduce the amount of costly real-world interactions required for convergence. We introduce Symbolic Real-Time Dynamic Programming (or sRTDP), an extension of RTDP. After each step of on-line interaction with an environment, sRTDP uses symbolic model-checking techniques to generalizes its experience by updating a group of states rather than …
As machine learning permeates more industries and models become more expensive and time consuming to train, the need for efficient automated hyperparameter optimization (HPO) has never been more pressing. Multi-step planning based approaches to hyperparameter optimization promise improved efficiency over myopic alternatives by more effectively balancing out exploration and exploitation. However, the potential of these approaches has not been fully realized due to their technical complexity and computational intensity. In this work, we leverage recent advances in Transformer-based, natural-lang…
Models Matter: The Impact of Single-Step Retrosynthesis on Synthesis Planning
Helmholtz Zentrum München（慕尼黑亥姆霍兹中心）；Janssen Research & Development, Janssen Pharmaceutica N.V（杨森研究与开发，杨森制药）；Leiden University（莱顿大学）；Pfizer Worldwide Research Development and Medical（辉瑞全球研究开发与医学）；AstraZeneca（阿斯利康）
PlanLLM: Video Procedure Planning with Refinable Large Language Models
Wangxuan Institute of Computer Technology, Peking University（北京大学王选计算机研究所）；State Key Laboratory of General Artificial Intelligence, Peking University（北京大学通用人工智能国家重点实验室）
University of California San Diego（加州大学圣地亚哥分校）；University of Cambridge（剑桥大学）
Conflict-Based Search is one of the most popular methods for multi-agent path finding. Though it is complete and optimal, it does not scale well. Recent works have been proposed to accelerate it by introducing various heuristics. However, whether these heuristics can apply to non-grid-based problem settings while maintaining their effectiveness remains an open question. In this work, we find that the answer is prone to be no. To this end, we propose a learning-based component, i.e., the Graph Transformer, as a heuristic function to accelerate the planning. The proposed method is provably compl…
Why Reasoning Fails to Plan: A Planning-Centric Analysis of Long-Horizon Decision Making in LLM Agents
University of Notre Dame（诺丁汉大学）；Stanford University（斯坦福大学）；Purdue University（普渡大学）；University of Edinburgh（爱丁堡大学）；University of Oxford（牛津大学）；Yale University（耶鲁大学）
University of California, Santa Barbara（加州大学圣巴巴拉分校）；University of California, Santa Cruz（加州大学圣克鲁兹分校）
Procedural planning aims to implement complex high-level goals by decomposition into sequential simpler low-level steps. Although procedural planning is a basic skill set for humans in daily life, it remains a challenge for large language models (LLMs) that lack a deep understanding of the cause-effect relations in procedures. Previous methods require manual exemplars to acquire procedural planning knowledge from LLMs in the zero-shot setting. However, such elicited pre-trained knowledge in LLMs induces spurious correlations between goals and steps, which impair the model generalization to uns…
Fast and scalable retrosynthetic planning with a transformer neural network and speculative beam search
SUPSI, IDSIA（SUPSI、IDSIA）；Pfizer Research and Development（辉瑞研发）；Institute for Digital Technologies for Personalized Healthcare（个性化医疗数字技术研究所）；KAUST（王国立科技大学）；Center for Generative AI（生成人工智能中心）
To prolong the lifetime of the unmanned aerial vehicles (UAVs), the UAVs need to fulfill their missions in the shortest possible time. In addition to this requirement, in many applications, the UAVs require a reliable internet connection during their flights. In this paper, we minimize the travel time of the UAVs, ensuring that a probabilistic connectivity constraint is satisfied. To solve this problem, we need a global model of the outage probability in the environment. Since the UAVs have different missions and fly over different areas, their collected data carry local information on the net…
NVIDIA（英伟达）；University of California San Diego（加州大学圣地亚哥分校）；University of Washington（华盛顿大学）
Robots will be expected to manipulate a wide variety of objects in complex and arbitrary ways as they become more widely used in human environments. As such, the rearrangement of objects has been noted to be an important benchmark for AI capabilities in recent years. We propose NeRP (Neural Rearrangement Planning), a deep learning based approach for multi-step neural object rearrangement planning which works with never-before-seen objects, that is trained on simulation data, and generalizes to the real world. We compare NeRP to several naive and model-based baselines, demonstrating that our ap…
FusionRetro: Molecule Representation Fusion via In-Context Learning for Retrosynthetic Planning
Pennsylvania State University（宾夕法尼亚州立大学）；Massachusetts Institute of Technology（麻省理工学院）；Stanford University（斯坦福大学）；Mila - Québec AI Institute（米拉-魁北克人工智能研究所）；Université de Montréal（蒙特利尔大学）；Yale University（耶鲁大学）；HEC Montréal（蒙特利尔高等商学院）；Tencent AI Lab（腾讯人工智能实验室）
Stanford University（斯坦福大学）；Nvidia（英伟达公司）；University of Toronto（多伦多大学）；Vector Institute（向量研究所）
The fundamental challenge of planning for multi-step manipulation is to find effective and plausible action sequences that lead to the task goal. We present Cascaded Variational Inference (CAVIN) Planner, a model-based method that hierarchically generates plans by sampling from latent spaces. To facilitate planning over long time horizons, our method learns latent representations that decouple the prediction of high-level effects from the generation of low-level motions through cascaded variational inference. This enables us to model dynamics at two different levels of temporal resolutions for…
