Search arXivSearch

arXiv · 2407.05789

CANDID DAC: Leveraging Coupled Action Dimensions with Importance Differences in DAC

Abstract

High-dimensional action spaces remain a challenge for dynamic algorithm configuration (DAC). Interdependencies and varying importance between action dimensions are further known key characteristics of DAC problems. We argue that these Coupled Action Dimensions with Importance Differences (CANDID) represent aspects of the DAC problem that are not yet fully explored. To address this gap, we introduce a new white-box benchmark within the DACBench suite that simulates the properties of CANDID. Further, we propose sequential policies as an effective strategy for managing these properties. Such policies factorize the action space and mitigate exponential growth by learning a policy per action dimension. At the same time, these policies accommodate the interdependence of action dimensions by fostering implicit coordination. We show this in an experimental study of value-based policies on our new benchmark. This study demonstrates that sequential policies significantly outperform independent learning of factorized policies in CANDID action spaces. In addition, they overcome the scalability limitations associated with learning a single policy across all action dimensions. The code used for our experiments is available under https://github.com/PhilippBordne/candidDAC.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Philipp Bordne, M. Asif Hasan, Eddie Bergman, Noor Awad, André Biedenkapp. 2024-09-17. CANDID DAC: Leveraging Coupled Action Dimensions with Importance Differences in DAC. https://arxiv.org/abs/2407.05789

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Analysis of Regularized Learning in Banach Spaces for Linear-functional Data

This article delves into the study of the theory of regularized learning in Banach spaces for linear-functional data. It encompasses discussions on representer theorems, pseudo-approximation theorems, and convergence theorems. Regularized learning is designed to minimize regularized empirical risks over a Banach space. The empirical risks are calculated by utilizing training data and multi-loss functions. The input training data are composed of linear functionals in a predual space of the Banach space to capture discrete local information from multimodal data and multiscale models. Through the regularized learning, approximations of the exact solution to an unidentified or uncertain original problem are globally achieved. In the convergence theorems, the convergence of the approximate solutions to the exact solution is established through the utilization of the weak* topology of the Banach space. The theorems of regularized learning are utilized in the interpretation of classical machine learning, such as support vector machines and artificial neural networks.

cs.LG

On Minimal Depth in Neural Networks

Understanding the relationship between the depth of a neural network and its representational capacity is a central problem in deep learning theory. In this work, we develop a geometric framework to analyze the expressivity of ReLU networks with the notion of depth complexity for convex polytopes. The depth of a polytope recursively quantifies the number of alternating convex hull and Minkowski sum operations required to construct it. This geometric perspective serves as a rigorous tool for deriving depth lower bounds and understanding the structural limits of deep neural architectures. We establish lower and upper bounds on the depth of polytopes, as well as tight bounds for classical families. These results yield two main consequences. First, we provide a purely geometric proof of the expressivity bound by Arora et al. (2018), confirming that $\lceil \log_2(n+1)\rceil$ hidden layers suffice to represent any continuous piecewise linear (CPWL) function. Second, we prove that, unlike general ReLU networks, convex polytopes do not admit a universal depth bound. Specifically, the depth of cyclic polytopes in dimensions $n \geq 4$ grows unboundedly with the number of vertices. This result implies that Input Convex Neural Networks (ICNNs) cannot represent all convex CPWL functions with a fixed depth, revealing a sharp separation in expressivity between ICNNs and standard ReLU networks.

cs.LG

DeepSPoC: A Deep Learning Based Sequential Propagation of Chaos

Classical particle methods based on propagation of chaos (PoC) have been developed for solving mean-field stochastic differential equations and their associated nonlinear Fokker--Planck equations. However, direct PoC implementations are difficult to apply to high-dimensional problems because they require simulating and storing large numbers of interacting particles, often with high particle-particle interaction costs. Motivated by these limitations, we build on the recently proposed sequential propagation of chaos (SPoC) framework, which replaces the fully interacting particle system in PoC with a sequential interaction mechanism. Based on this structure, we present DeepSPoC, a neural particle method that embeds a neural density representation into the sequential particle dynamics. DeepSPoC simulates particles batch by batch, while the neural network represents the evolving empirical law and is substituted into the coefficients of the mean-field SDE, thereby replacing direct particle-particle interactions with particle-network interactions. In DeepSPoC, a recently developed normalizing flow model called KRnet is used to approximate the empirical measure of particles. Compared with direct particle implementations, DeepSPoC substantially reduces memory consumption and evaluates interaction terms more efficiently, thereby improving scalability for high-dimensional problems. We apply DeepSPoC to a wide range of mean-field equations and verify its effectiveness and computational advantages.

cs.LG