Value Iteration (VI) is one of the most classic algorithms for solving Markov Decision Processes (MDPs), which lays the foundations for various more advanced reinforcement learning algorithms, such as Q-learning. VI may take a large number of iterations to converge as it is a first-order method. In this paper, we introduce the Newton Value Iteration (NVI) algorithm, which eliminates the impact of action space dimension compared to some previous second-order methods. Consequently, NVI can efficiently handle MDPs with large action spaces. Building upon NVI, we propose a novel approach called Sketched Newton Value Iteration (SNVI) to tackle MDPs with both large state and action spaces. SNVI not only inherits the stability and fast convergence advantages of second-order algorithms, but also significantly reduces computational complexity, making it highly scalable. Extensive experiments demonstrate the superiority of our algorithms over traditional VI and previously proposed second-order VI algorithms.

Sketched Newton Value Iteration for Large-Scale Markov Decision Processes

Linear programming has been practically solved mainly by simplex and interior point methods. Compared with the weakly polynomial complexity obtained by the interior point methods, the existence of strongly polynomial bounds for the length of the pivot path generated by the simplex methods remains a mystery. In this paper, we propose two novel pivot experts that leverage both global and local information of the linear programming instances for the primal simplex method and show their excellent performance numerically. The experts can be regarded as a benchmark to evaluate the performance of classical pivot rules, although they are hard to directly implement. To tackle this challenge, we employ a graph convolutional neural network model, trained via imitation learning, to mimic the behavior of the pivot expert. Our pivot rule, learned empirically, displays a significant advantage over conventional methods in various linear programming problems, as demonstrated through a series of rigorous experiments.

Learning to Pivot as a Smart Expert | VIDEO

In many important machine learning applications, the standard assumption of having a globally Lipschitz continuous gradient may fail to hold. This paper delves into a more general $(L_0, L_1)$-smoothness setting, which gains particular significance within the realms of deep neural networks and distributionally robust optimization (DRO).  We demonstrate the significant advantage of trust region methods for stochastic nonconvex optimization under such generalized smoothness assumption.
    We show that first-order trust region methods can recover the normalized and clipped stochastic gradient as special cases and then provide a unified analysis to show their convergence to first-order stationary conditions.
    Motivated by the important application of DRO, we propose a generalized high-order smoothness condition, under which second-order trust region methods can achieve a complexity of $\mathcal{O}(\epsilon^{-3.5})$ for convergence to  second-order stationary points. By incorporating variance reduction,  the second-order trust region method obtains an even better complexity of $\mathcal{O}(\epsilon^{-3})$, matching the optimal bound for standard smooth optimization. To our best knowledge, this is the first work to show convergence beyond the first-order stationary condition for generalized smooth optimization.
    Preliminary experiments show that our proposed algorithms perform favorably compared with existing methods.

Trust Region Methods for Nonconvex Stochastic Optimization beyond Lipschitz Smoothness

Main Track - Machine Learning

technical paper

We are pleased to announce the Thirty-Eighth AAAI Conference on Artificial Intelligence (AAAI-24), which will be held in Vancouver, British Columbia at the Vancouver Convention Centre – West Building from 20-27 February, 2024.

The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines. AAAI-24 will feature technical paper presentations, special tracks, invited speakers, workshops, tutorials, poster sessions, senior member presentations, competitions, and exhibit programs, and a range of other activities to be announced.

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AAAI 2024

The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines. 

Yinyu Ye

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Presentations

Sketched Newton Value Iteration for Large-Scale Markov Decision Processes

Learning to Pivot as a Smart Expert | VIDEO

Trust Region Methods for Nonconvex Stochastic Optimization beyond Lipschitz Smoothness

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