Related papers: A Closed-Form Upper Bound for Admissible Learning-…
Online decision making under uncertainty in partially observable domains, also known as Belief Space Planning, is a fundamental problem in robotics and Artificial Intelligence. Due to an abundance of plausible future unravelings,…
We build a theoretical framework for designing and understanding practical meta-learning methods that integrates sophisticated formalizations of task-similarity with the extensive literature on online convex optimization and sequential…
A key impediment to reinforcement learning (RL) in real applications with limited, batch data is defining a reward function that reflects what we implicitly know about reasonable behaviour for a task and allows for robust off-policy…
We suggest an iterative approach to computing K-step maximum likelihood estimates (MLE) of the parametric components in semiparametric models based on their profile likelihoods. The higher order convergence rate of K-step MLE mainly depends…
Current approaches for training Process Reward Models (PRMs) often involve breaking down responses into multiple reasoning steps using rule-based techniques, such as using predefined placeholder tokens or setting the reasoning step's length…
We establish finite-step probabilistic upper bounds on the contraction ratios $\rho_k = \Delta_{k+1}/\Delta_k$ for iterated Pearson correlation dynamics. Let $(P_k)_{k\ge 0}$ be the sequence generated by the Pearson update. Define $\Delta_k…
We develop minimax optimal risk bounds for the general learning task consisting in predicting as well as the best function in a reference set G up to the smallest possible additive term, called the convergence rate. When the reference set…
We study the connection between gradient-based meta-learning and convex op-timisation. We observe that gradient descent with momentum is a special case of meta-gradients, and building on recent results in optimisation, we prove convergence…
Closed-loop learning is the process of repeatedly estimating a model from data generated from the model itself. It is receiving great attention due to the possibility that large neural network models may, in the future, be primarily trained…
Gradient-based iterative optimization methods are the workhorse of modern machine learning. They crucially rely on careful tuning of parameters like learning rate and momentum. However, one typically sets them using heuristic approaches…
We prove risk bounds for binary classification in high-dimensional settings when the sample size is allowed to be smaller than the dimensionality of the training set observations. In particular, we prove upper bounds for both 'compressive…
We study the convergence rate of Bregman gradient methods for convex optimization in the space of measures on a $d$-dimensional manifold. Under basic regularity assumptions, we show that the suboptimality gap at iteration $k$ is in…
Inference is typically intractable in high-treewidth undirected graphical models, making maximum likelihood learning a challenge. One way to overcome this is to restrict parameters to a tractable set, most typically the set of…
Reachability computations that rely on learned or estimated models require calibration in order to uphold confidence about their guarantees. Calibration generally involves sampling scenarios inside the reachable set. However, producing…
In many iterative optimization methods, fixed-point theory enables the analysis of the convergence rate via the contraction factor associated with the linear approximation of the fixed-point operator. While this factor characterizes the…
Newton-step approximations to pseudo maximum likelihood estimates of spatial autoregressive models with a large number of parameters are examined, in the sense that the parameter space grows slowly as a function of sample size. These have…
As a popular meta-learning approach, the model-agnostic meta-learning (MAML) algorithm has been widely used due to its simplicity and effectiveness. However, the convergence of the general multi-step MAML still remains unexplored. In this…
In this paper, we examine an important problem of learning neural networks that certifiably meet certain specifications on input-output behaviors. Our strategy is to find an inner approximation of the set of admissible policy parameters,…
There is a large body of evidence that decision makers frequently depart from Bayesian updating. This paper introduces a model, robust maximum likelihood (RML) updating, where deviations from Bayesian updating are due to multiple…
We address the challenge of optimizing meta-parameters (hyperparameters) in machine learning, a key factor for efficient training and high model performance. Rather than relying on expensive meta-parameter search methods, we introduce…