86,820 research outputs found
Deep Gaussian processes for regression using approximate expectation propagation
Deep Gaussian processes (DGPs) are multi-layer hierarchical generalisations
of Gaussian processes (GPs) and are formally equivalent to neural networks with
multiple, infinitely wide hidden layers. DGPs are nonparametric probabilistic
models and as such are arguably more flexible, have a greater capacity to
generalise, and provide better calibrated uncertainty estimates than
alternative deep models. This paper develops a new approximate Bayesian
learning scheme that enables DGPs to be applied to a range of medium to large
scale regression problems for the first time. The new method uses an
approximate Expectation Propagation procedure and a novel and efficient
extension of the probabilistic backpropagation algorithm for learning. We
evaluate the new method for non-linear regression on eleven real-world
datasets, showing that it always outperforms GP regression and is almost always
better than state-of-the-art deterministic and sampling-based approximate
inference methods for Bayesian neural networks. As a by-product, this work
provides a comprehensive analysis of six approximate Bayesian methods for
training neural networks
Hierarchical Deep Counterfactual Regret Minimization
Imperfect Information Games (IIGs) offer robust models for scenarios where
decision-makers face uncertainty or lack complete information. Counterfactual
Regret Minimization (CFR) has been one of the most successful family of
algorithms for tackling IIGs. The integration of skill-based strategy learning
with CFR could potentially enhance learning performance for complex IIGs. For
this, a hierarchical strategy needs to be learnt, wherein low-level components
represent specific skills and the high-level component manages the transition
between skills. This hierarchical approach also enhances interpretability,
helping humans pinpoint scenarios where the agent is struggling and intervene
with targeted expertise. This paper introduces the first hierarchical version
of Deep CFR (HDCFR), an innovative method that boosts learning efficiency in
tasks involving extensively large state spaces and deep game trees. A notable
advantage of HDCFR over previous research in this field is its ability to
facilitate learning with predefined (human) expertise and foster the
acquisition of transferable skills that can be applied to similar tasks. To
achieve this, we initially construct our algorithm on a tabular setting,
encompassing hierarchical CFR updating rules and a variance-reduced Monte-Carlo
sampling extension, and offer its essential theoretical guarantees. Then, to
adapt our algorithm for large-scale applications, we employ neural networks as
function approximators and suggest deep learning objectives that coincide with
those in the tabular setting while maintaining the theoretical outcomes
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