A Markovian Model for Learning-to-Optimize

• URL: http://arxiv.org/abs/2408.11629v1
• Date: Wed, 21 Aug 2024 14:00:22 GMT
• Title: A Markovian Model for Learning-to-Optimize
• Authors: Michael Sucker, Peter Ochs,
• Abstract summary: We present a probabilistic model for iterative algorithms with the use case of optimization algorithms in mind. Based on this model, we present PAC-Bayesian generalization bounds for functions that are defined on the trajectory of the learned algorithm.
• Score: 4.112909937203119
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a probabilistic model for stochastic iterative algorithms with the use case of optimization algorithms in mind. Based on this model, we present PAC-Bayesian generalization bounds for functions that are defined on the trajectory of the learned algorithm, for example, the expected (non-asymptotic) convergence rate and the expected time to reach the stopping criterion. Thus, not only does this model allow for learning stochastic algorithms based on their empirical performance, it also yields results about their actual convergence rate and their actual convergence time. We stress that, since the model is valid in a more general setting than learning-to-optimize, it is of interest for other fields of application, too. Finally, we conduct five practically relevant experiments, showing the validity of our claims.

Related papers

• Efficient Fairness-Performance Pareto Front Computation [51.558848491038916]
  We show that optimal fair representations possess several useful structural properties. We then show that these approxing problems can be solved efficiently via concave programming methods.
  arXiv  Detail & Related papers  (2024-09-26T08:46:48Z)
• Asymptotically Efficient Online Learning for Censored Regression Models Under Non-I.I.D Data [2.2446129622980227]
  An efficient online learning problem is investigated for censored regression models. A numerical example is provided to illustrate the superiority of the proposed online algorithm over the existing related ones in the literature.
  arXiv  Detail & Related papers  (2023-09-18T03:28:48Z)
• Learning Unnormalized Statistical Models via Compositional Optimization [73.30514599338407]
  Noise-contrastive estimation(NCE) has been proposed by formulating the objective as the logistic loss of the real data and the artificial noise. In this paper, we study it a direct approach for optimizing the negative log-likelihood of unnormalized models.
  arXiv  Detail & Related papers  (2023-06-13T01:18:16Z)
• Representation Learning with Multi-Step Inverse Kinematics: An Efficient and Optimal Approach to Rich-Observation RL [106.82295532402335]
  Existing reinforcement learning algorithms suffer from computational intractability, strong statistical assumptions, and suboptimal sample complexity. We provide the first computationally efficient algorithm that attains rate-optimal sample complexity with respect to the desired accuracy level. Our algorithm, MusIK, combines systematic exploration with representation learning based on multi-step inverse kinematics.
  arXiv  Detail & Related papers  (2023-04-12T14:51:47Z)
• A bandit-learning approach to multifidelity approximation [7.960229223744695]
  Multifidelity approximation is an important technique in scientific computation and simulation. We introduce a bandit-learning approach for leveraging data of varying fidelities to achieve precise estimates.
  arXiv  Detail & Related papers  (2021-03-29T05:29:35Z)
• Asymptotic study of stochastic adaptive algorithm in non-convex landscape [2.1320960069210484]
  This paper studies some assumption properties of adaptive algorithms widely used in optimization and machine learning. Among them Adagrad and Rmsprop, which are involved in most of the blackbox deep learning algorithms.
  arXiv  Detail & Related papers  (2020-12-10T12:54:45Z)
• SODEN: A Scalable Continuous-Time Survival Model through Ordinary Differential Equation Networks [14.564168076456822]
  We propose a flexible model for survival analysis using neural networks along with scalable optimization algorithms. We demonstrate the effectiveness of the proposed method in comparison to existing state-of-the-art deep learning survival analysis models.
  arXiv  Detail & Related papers  (2020-08-19T19:11:25Z)
• Control as Hybrid Inference [62.997667081978825]
  We present an implementation of CHI which naturally mediates the balance between iterative and amortised inference. We verify the scalability of our algorithm on a continuous control benchmark, demonstrating that it outperforms strong model-free and model-based baselines.
  arXiv  Detail & Related papers  (2020-07-11T19:44:09Z)
• Adaptive Discretization for Model-Based Reinforcement Learning [10.21634042036049]
  We introduce the technique of adaptive discretization to design an efficient model-based episodic reinforcement learning algorithm. Our algorithm is based on optimistic one-step value iteration extended to maintain an adaptive discretization of the space.
  arXiv  Detail & Related papers  (2020-07-01T19:36:46Z)
• Slice Sampling for General Completely Random Measures [74.24975039689893]
  We present a novel Markov chain Monte Carlo algorithm for posterior inference that adaptively sets the truncation level using auxiliary slice variables. The efficacy of the proposed algorithm is evaluated on several popular nonparametric models.
  arXiv  Detail & Related papers  (2020-06-24T17:53:53Z)
• Model-Augmented Actor-Critic: Backpropagating through Paths [81.86992776864729]
  Current model-based reinforcement learning approaches use the model simply as a learned black-box simulator. We show how to make more effective use of the model by exploiting its differentiability.
  arXiv  Detail & Related papers  (2020-05-16T19:18:10Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.