The selected locations are highlighted, while other U.S. locations are also plotted for comparison. Regions with both high CV and high average carbon intensity are identified as prime targets for DRL agents to maximize their impact on reducing carbon emissions. In the table bellow (7) is the summarizing the selected locations, typical weather values, and carbon emissions characteristics: Considering the data from (9), the U.S. states with the highest number of data centers are summarized in Table 8. The states with the most significant number of data centers tend to be Virginia, Texas, California, and New York. Virginia, especially, is a major hub due to its proximity to Washington D.C. and the abundance of fiber optic cable networks. Texas and California are also prominent due to their size, economic output, and significant tech industries. New York, particularly around New York City, hosts numerous data centers that serve the financial sector and other industries. The selection of these locations is justified by their significant number of data centers, which emphasizes the potential impact of DRL agents in these regions. By targeting areas with both high data center density and favorable carbon intensity characteristics, DRL agents can maximize their effectiveness in reducing carbon emissions.

Machine learning has driven an exponential increase in computational demand, leading to massive data centers that consume significant energy and contribute to climate change. This makes sustainable data center control a priority. In this paper, we introduce SustainDC, a set of Python environments for benchmarking multiagent reinforcement learning (MARL) algorithms for data centers (DC). SustainDC supports custom DC configurations and tasks such as workload scheduling, cooling optimization, and auxiliary battery management, with multiple agents managing these operations while accounting for the effects of each other. We evaluate various MARL algorithms on SustainDC, showing their performance across diverse DC designs, locations, weather conditions, grid carbon intensity, and workload requirements. Our results highlight significant opportunities to improve data center operations using MARL algorithms. Given the increasing use of DC due to AI, SustainDC provides a crucial platform for developing and benchmarking advanced algorithms essential for achieving sustainable computing and addressing other heterogeneous real-world challenges.

We introduce a new stochastic multi-armed bandit setting where arms are grouped inside "ordered" categories. The motivating example comes from e-commerce, where a customer typically has a greater appetence for items of a specific wellidentified but unknown category than any other one. We introduce three concepts of ordering between categories, inspired by stochastic dominance between random variables, which are gradually weaker so that more and more bandit scenarios satisfy at least one of them. We first prove instance-dependent lower bounds on the cumulative regret for each of these models, indicating how the complexity of the bandit problems increases with the generality of the ordering concept considered. We also provide algorithms that fully leverage the structure of the model with their associated theoretical guarantees. Finally, we have conducted an analysis on real data to highlight that those ordered categories actually exist in practice.

Decision-making in large-scale games is an essential research area in artificial intelligence (AI) with significant real-world impact. However, the limited access to realistic large-scale game environments has hindered research progress in this area. In this paper, we present AuctionNet, a benchmark for bid decision-making in largescale ad auctions derived from a real-world online advertising platform. AuctionNet is composed of three parts: an ad auction environment, a pre-generated dataset based on the environment, and performance evaluations of several baseline bid decision-making algorithms. More specifically, the environment effectively replicates the integrity and complexity of real-world ad auctions through the interaction of several modules: the ad opportunity generation module employs deep generative networks to bridge the gap between simulated and real-world data while mitigating the risk of sensitive data exposure; the bidding module implements diverse autobidding agents trained with different decision-making algorithms; and the auction module is anchored in the classic Generalized Second Price (GSP) auction but also allows for customization of auction mechanisms as needed.

Symmetries are prevalent in deep learning and can significantly influence the learning dynamics of neural networks. In this paper, we examine how exponential symmetries - a broad subclass of continuous symmetries present in the model architecture or loss function - interplay with stochastic gradient descent (SGD). We first prove that gradient noise creates a systematic motion (a "Noether flow") of the parameters θ along the degenerate direction to a unique initializationindependent fixed point θ

The spectral clustering algorithm for directed networks that we consider in this paper is shown in Algorithm A.1. This algorithm is used for the community detection step in our proposed CHIP estimation procedure. For undirected networks, which we use for the theoretical analysis in Section 4, spectral clustering is performed by running k-means clustering on the rows of the eigenvector matrix of N or A, not the rows of the concatenated singular vector matrix. The three parameters µ, α, β can be estimated by maximizing (A.1) using standard numerical methods for non-linear optimization (Nocedal & Wright, 2006). In our CHIP model, we have separate (µ, α, β) parameters for each block pair (a, b).

In many application settings involving networks, such as messages between users of an on-line social network or transactions between traders in financial markets, the observed data consist of timestamped relational events, which form a continuoustime network. We propose the Community Hawkes Independent Pairs (CHIP) generative model for such networks. We show that applying spectral clustering to an aggregated adjacency matrix constructed from the CHIP model provides consistent community detection for a growing number of nodes and time duration. We also develop consistent and computationally efficient estimators for the model parameters. We demonstrate that our proposed CHIP model and estimation procedure scales to large networks with tens of thousands of nodes and provides superior fits than existing continuous-time network models on several real networks.

The standard paradigm of modeling marked point processes is by parameterizing the intensity function using an attention-based (Transformer-style) architecture. Despite the flexibility of these methods, their inference is based on the computationally intensive thinning algorithm. In this work, we propose a framework where the advantages of the attention-based architecture are maintained and the limitation of the thinning algorithm is circumvented. The framework depends on modeling the conditional distribution of inter-event times with a mixture of log-normals satisfying a Markov property and the conditional probability mass function for the marks with a Transformer-based architecture. The proposed method attains state-of-the-art performance in predicting the next event of a sequence given its history. The experiments also reveal the efficacy of the methods that do not rely on the thinning algorithm during inference over the ones they do. Finally, we test our method on the challenging long-horizon prediction task and find that it outperforms a baseline developed specifically for tackling this task; importantly, inference requires just a fraction of time compared to the thinning-based baseline.

Despite many years of research into latent Dirichlet allocation (LDA), applying LDA to collections of non-categorical items is still challenging. Yet many problems with much richer data share a similar structure and could benefit from the vast literature on LDA. We propose logistic LDA, a novel discriminative variant of latent Dirichlet allocation which is easy to apply to arbitrary inputs. In particular, our model can easily be applied to groups of images, arbitrary text embeddings, and integrates well with deep neural networks. Although it is a discriminative model, we show that logistic LDA can learn from unlabeled data in an unsupervised manner by exploiting the group structure present in the data. In contrast to other recent topic models designed to handle arbitrary inputs, our model does not sacrifice the interpretability and principled motivation of LDA.

We study the problem of node classification on graphs with few-shot novel labels, which has two distinctive properties: (1) There are novel labels to emerge in the graph; (2) The novel labels have only a few representative nodes for training a classifier. The study of this problem is instructive and corresponds to many applications such as recommendations for newly formed groups with only a few users in online social networks. To cope with this problem, we propose a novel Meta Transformed Network Embedding framework (MetaTNE), which consists of three modules: (1) A structural module provides each node a latent representation according to the graph structure.