Modern Reinforcement Learning (RL) algorithms are able to outperform humans in a wide variety of tasks. Multi-agent reinforcement learning (MARL) settings present additional challenges, and successful cooperation in mixed-motive groups of agents depends on a delicate balancing act between individual and group objectives. Social conventions and norms, often inspired by human institutions, are used as tools for striking this balance. In this paper, we examine a fundamental, well-studied social convention that underlies cooperation in both animal and human societies: Dominance hierarchies. We adapt the ethological theory of dominance hierarchies to artificial agents, borrowing the established terminology and definitions with as few amendments as possible. We demonstrate that populations of RL agents, operating without explicit programming or intrinsic rewards, can invent, learn, enforce, and transmit a dominance hierarchy to new populations. The dominance hierarchies that emerge have a similar structure to those studied in chickens, mice, fish, and other species.
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The Stochastic Gradient Descent method (SGD) and its stochastic variants have become methods of choice for solving finite-sum optimization problems arising from machine learning and data science thanks to their ability to handle large-scale applications and big datasets. In the last decades, researchers have made substantial effort to study the theoretical performance of SGD and its shuffling variants. However, only limited work has investigated its shuffling momentum variants, including shuffling heavy-ball momentum schemes for non-convex problems and Nesterov's momentum for convex settings. In this work, we extend the analysis of the shuffling momentum gradient method developed in [Tran et al (2021)] to both finite-sum convex and strongly convex optimization problems. We provide the first analysis of shuffling momentum-based methods for the strongly convex setting, attaining a convergence rate of $O(1/nT^2)$, where $n$ is the number of samples and $T$ is the number of training epochs. Our analysis is a state-of-the-art, matching the best rates of existing shuffling stochastic gradient algorithms in the literature.
Machine learning (ML) provides powerful tools for predictive modeling. ML's popularity stems from the promise of sample-level prediction with applications across a variety of fields from physics and marketing to healthcare. However, if not properly implemented and evaluated, ML pipelines may contain leakage typically resulting in overoptimistic performance estimates and failure to generalize to new data. This can have severe negative financial and societal implications. Our aim is to expand understanding associated with causes leading to leakage when designing, implementing, and evaluating ML pipelines. Illustrated by concrete examples, we provide a comprehensive overview and discussion of various types of leakage that may arise in ML pipelines.
We consider $k$-Facility Location games, where $n$ strategic agents report their locations on the real line, and a mechanism maps them to $k\ge 2$ facilities. Each agent seeks to minimize her distance to the nearest facility. We are interested in (deterministic or randomized) strategyproof mechanisms without payments that achieve a reasonable approximation ratio to the optimal social cost of the agents. To circumvent the inapproximability of $k$-Facility Location by deterministic strategyproof mechanisms, we restrict our attention to perturbation stable instances. An instance of $k$-Facility Location on the line is $\gamma$-perturbation stable (or simply, $\gamma$-stable), for some $\gamma\ge 1$, if the optimal agent clustering is not affected by moving any subset of consecutive agent locations closer to each other by a factor at most $\gamma$. We show that the optimal solution is strategyproof in $(2+\sqrt{3})$-stable instances whose optimal solution does not include any singleton clusters, and that allocating the facility to the agent next to the rightmost one in each optimal cluster (or to the unique agent, for singleton clusters) is strategyproof and $(n-2)/2$-approximate for $5$-stable instances (even if their optimal solution includes singleton clusters). On the negative side, we show that for any $k\ge 3$ and any $\delta > 0$, there is no deterministic anonymous mechanism that achieves a bounded approximation ratio and is strategyproof in $(\sqrt{2}-\delta)$-stable instances. We also prove that allocating the facility to a random agent of each optimal cluster is strategyproof and $2$-approximate in $5$-stable instances. To the best of our knowledge, this is the first time that the existence of deterministic (resp. randomized) strategyproof mechanisms with a bounded (resp. constant) approximation ratio is shown for a large and natural class of $k$-Facility Location instances.
Game-theoretic dynamics between AI agents could differ from traditional human-human interactions in various ways. One such difference is that it may be possible to accurately simulate an AI agent, for example because its source code is known. Our aim is to explore ways of leveraging this possibility to achieve more cooperative outcomes in strategic settings. In this paper, we study an interaction between AI agents where the agents run a recursive joint simulation. That is, the agents first jointly observe a simulation of the situation they face. This simulation in turn recursively includes additional simulations (with a small chance of failure, to avoid infinite recursion), and the results of all these nested simulations are observed before an action is chosen. We show that the resulting interaction is strategically equivalent to an infinitely repeated version of the original game, allowing a direct transfer of existing results such as the various folk theorems.
Variational Quantum Algorithms (VQAs) may be a path to quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) computers. A natural question is whether noise on NISQ devices places fundamental limitations on VQA performance. We rigorously prove a serious limitation for noisy VQAs, in that the noise causes the training landscape to have a barren plateau (i.e., vanishing gradient). Specifically, for the local Pauli noise considered, we prove that the gradient vanishes exponentially in the number of qubits $n$ if the depth of the ansatz grows linearly with $n$. These noise-induced barren plateaus (NIBPs) are conceptually different from noise-free barren plateaus, which are linked to random parameter initialization. Our result is formulated for a generic ansatz that includes as special cases the Quantum Alternating Operator Ansatz and the Unitary Coupled Cluster Ansatz, among others. For the former, our numerical heuristics demonstrate the NIBP phenomenon for a realistic hardware noise model.
Uniformity plays a crucial role in the assessment of learned representations, contributing to a deeper comprehension of self-supervised learning. The seminal work by \citet{Wang2020UnderstandingCR} introduced a uniformity metric that quantitatively measures the collapse degree of learned representations. Directly optimizing this metric together with alignment proves to be effective in preventing constant collapse. However, we present both theoretical and empirical evidence revealing that this metric lacks sensitivity to dimensional collapse, highlighting its limitations. To address this limitation and design a more effective uniformity metric, this paper identifies five fundamental properties, some of which the existing uniformity metric fails to meet. We subsequently introduce a novel uniformity metric that satisfies all of these desiderata and exhibits sensitivity to dimensional collapse. When applied as an auxiliary loss in various established self-supervised methods, our proposed uniformity metric consistently enhances their performance in downstream tasks.Our code was released at //github.com/sunset-clouds/WassersteinUniformityMetric.
A Large Language Model (LLM) is considered consistent if semantically equivalent prompts produce semantically equivalent responses. Despite recent advancements showcasing the impressive capabilities of LLMs in conversational systems, we show that even state-of-the-art LLMs are highly inconsistent in their generations, questioning their reliability. Prior research has tried to measure this with task-specific accuracy. However, this approach is unsuitable for moral scenarios, such as the trolley problem, with no "correct" answer. To address this issue, we propose a novel information-theoretic measure called Semantic Graph Entropy (SGE) to measure the consistency of an LLM in moral scenarios. We leverage "Rules of Thumb" (RoTs) to explain a model's decision-making strategies and further enhance our metric. Compared to existing consistency metrics, SGE correlates better with human judgments across five LLMs. In the future, we aim to investigate the root causes of LLM inconsistencies and propose improvements.
Weakly supervised phrase grounding aims at learning region-phrase correspondences using only image-sentence pairs. A major challenge thus lies in the missing links between image regions and sentence phrases during training. To address this challenge, we leverage a generic object detector at training time, and propose a contrastive learning framework that accounts for both region-phrase and image-sentence matching. Our core innovation is the learning of a region-phrase score function, based on which an image-sentence score function is further constructed. Importantly, our region-phrase score function is learned by distilling from soft matching scores between the detected object class names and candidate phrases within an image-sentence pair, while the image-sentence score function is supervised by ground-truth image-sentence pairs. The design of such score functions removes the need of object detection at test time, thereby significantly reducing the inference cost. Without bells and whistles, our approach achieves state-of-the-art results on the task of visual phrase grounding, surpassing previous methods that require expensive object detectors at test time.
Graph Neural Networks (GNNs) have been shown to be effective models for different predictive tasks on graph-structured data. Recent work on their expressive power has focused on isomorphism tasks and countable feature spaces. We extend this theoretical framework to include continuous features - which occur regularly in real-world input domains and within the hidden layers of GNNs - and we demonstrate the requirement for multiple aggregation functions in this context. Accordingly, we propose Principal Neighbourhood Aggregation (PNA), a novel architecture combining multiple aggregators with degree-scalers (which generalize the sum aggregator). Finally, we compare the capacity of different models to capture and exploit the graph structure via a novel benchmark containing multiple tasks taken from classical graph theory, alongside existing benchmarks from real-world domains, all of which demonstrate the strength of our model. With this work, we hope to steer some of the GNN research towards new aggregation methods which we believe are essential in the search for powerful and robust models.
Embedding models for deterministic Knowledge Graphs (KG) have been extensively studied, with the purpose of capturing latent semantic relations between entities and incorporating the structured knowledge into machine learning. However, there are many KGs that model uncertain knowledge, which typically model the inherent uncertainty of relations facts with a confidence score, and embedding such uncertain knowledge represents an unresolved challenge. The capturing of uncertain knowledge will benefit many knowledge-driven applications such as question answering and semantic search by providing more natural characterization of the knowledge. In this paper, we propose a novel uncertain KG embedding model UKGE, which aims to preserve both structural and uncertainty information of relation facts in the embedding space. Unlike previous models that characterize relation facts with binary classification techniques, UKGE learns embeddings according to the confidence scores of uncertain relation facts. To further enhance the precision of UKGE, we also introduce probabilistic soft logic to infer confidence scores for unseen relation facts during training. We propose and evaluate two variants of UKGE based on different learning objectives. Experiments are conducted on three real-world uncertain KGs via three tasks, i.e. confidence prediction, relation fact ranking, and relation fact classification. UKGE shows effectiveness in capturing uncertain knowledge by achieving promising results on these tasks, and consistently outperforms baselines on these tasks.
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