Related papers: Realizability algebras III: some examples
We initiate the mathematical study of replicability as an algorithmic property in the context of reinforcement learning (RL). We focus on the fundamental setting of discounted tabular MDPs with access to a generative model. Inspired by…
We consider interactive learning in the realizable setting and develop a general framework to handle problems ranging from best arm identification to active classification. We begin our investigation with the observation that agnostic…
This paper investigates how global decision problems over arithmetically represented domains acquire reflective structure through class-quantification. Arithmetization forces diagonal fixed points whose verification requires reflection…
Fitting models to data is an important part of the practice of science. Advances in machine learning have made it possible to fit more -- and more complex -- models, but have also exacerbated a problem: when multiple models fit the data…
There is a third way of implementing probability models and practicing. This is to answer questions put in terms of observables. This eliminates frequentist hypothesis testing and Bayes factors and it also eliminates parameter estimation.…
A new method based on the rejection sampling for finding statistical tests is proposed. This method is conceptually intuitive, easy to implement, and applicable for arbitrary dimension. To illustrate its potential applicability, three…
Among the different possible strategies for evaluating the reliability of individual predictions of classifiers, robustness quantification stands out as a method that evaluates how much uncertainty a classifier could cope with before…
This article is concerned with the application of the program extraction technique to a new class of problems: the synthesis of decision procedures for the classical satisfiability problem that are correct by construction. To this end, we…
Composite likelihoods are a class of alternatives to the full likelihood which are widely used in many situations in which the likelihood itself is intractable. A composite likelihood may be computed without the need to specify the full…
Some more general "inheritance conditions" have been found for a given set of symmetry generators $\{\mathbf{Z}_{\bar{l}}\}$ acting on some set of coupled ordinary differential equations, once the "first integration method" has been applied…
Deep neural classifiers have recently found tremendous success in data-driven control systems. However, existing models suffer from a trade-off between accuracy and adversarial robustness. This limitation must be overcome in the control of…
In causal matching designs, some control subjects are often left unmatched, and some covariates are often left unmodeled. This article introduces "rebar," a method using high-dimensional modeling to incorporate these commonly discarded data…
Hierarchical reinforcement learning (HRL) has seen widespread interest as an approach to tractable learning of complex modular behaviors. However, existing work either assume access to expert-constructed hierarchies, or use…
The existing fractional grey prediction models mainly use discrete fractional-order difference and accumulation, but in the actual modeling, continuous fractional-order calculus has been proved to have many excellent properties, such as…
In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constructions of objects with such properties are often very difficult, or…
Model-based offline optimization with dynamics-aware policy provides a new perspective for policy learning and out-of-distribution generalization, where the learned policy could adapt to different dynamics enumerated at the training stage.…
Neural networks achieve outstanding accuracy in classification and regression tasks. However, understanding their behavior still remains an open challenge that requires questions to be addressed on the robustness, explainability and…
We show that Dependent Choice is a sufficient choice principle for developing the basic theory of proper forcing, and for deriving generic absoluteness for the Chang model in the presence of large cardinals, even with respect to…
We construct a geometric system from which the Hall algebra can be recovered. This system inherently satisfies higher associativity conditions and thus leads to a categorification of the Hall algebra. We then suggest how to use this…
Alignment has quickly become a default ingredient in LLM development, with techniques such as reinforcement learning from human feedback making models act safely, follow instructions, and perform ever-better on complex tasks. While these…