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Recent Submissions

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    Learning to best reply: On the consistency of multi-agent reinforcement learning
    (University of Waterloo, 2023-08-10) Possnig, Clemens
    This paper provides asymptotic results for a class of model-free actor-critic batch - reinforcement learning algorithms in the multi-agent setting. At each period, each agent faces an estimation problem (the critic, e.g. a value function), and a policy updating problem. The estimation step is done by parametric function estimation based on a bath of past observations. Agents have no knowledge of each others incentives and policies. I provide sufficient conditions for each agent's parametric function estimator to be consistent in the multi-agent environment, which enables agents to learn to best respond despite the non-stationarity inherent in multi-agent systems. The conditions depend on the environment, batch size, and policy step size. These sufficient conditions are useful in the asymptotic analysis of multi-agent learning, e.g. in the application of long-run characterisations using stochastic approximation techniques.
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    Reinforcement learning and collusion
    (University of Waterloo, 2023-07-24) Possnig, Clemens
    This paper presents an analytical characterization of the long rung policies learned by algorithms that interact repeatedly. These algorithms update policies which are maps from observed states to actions. I show that the long rung policies correspond to equilibria that are stable points of a tractable differential equation. As a running example, I consider a repeated Cournot game of quantity competition, for which learning the stage game Nash equilibrium serves as a non-collusive benchmark. I give necessary and sufficient conditions for this Nash equilibrium not to be learned. These are requirements on the state variables algorithms use to determine their actions, and on the stage game. When algorithms determine actions based only on the past period's price, the Nash equilibrium can be learned. However, agents may condition their actions on richer types of information beyond the past period's price. In that case, I give sufficient conditions such that the policies coverage with positive probability to a collusive equilibrium, while never converging to the Nash equilibrium.
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    A rational inattention theory of echo chamber
    (University of Waterloo, 2023-07) Hu, Lin; Li, Anqi; Tan, Xu
    We develop a rational inattention theory of echo chamber, whereby players gather information about an uncertain state by allocating limited attention capacities across biased primary sources and the other players. The resulting Poisson attention network transmits information from the primary source to a player either directly or indirectly through the other players. Rational inattention generates heterogeneous demands for information among players who are initially biased towards different decisions. In an echo chamber equilibrium, each player restricts attention to his own-biased source and like-minded friends, as the latter attend to the same primary source as his, and so could serve as secondary sources in case the information transmission from the primary source to him is disrupted. We provide sufficient conditions that give rise to echo chamber equilibria, characterize the attention networks within echo chambers, and use our results to inform the design and regulation of information platforms.
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    Parallel Efficient Secure DBSCAN Approximation
    (University of Waterloo, 2026-07-07) Shehata, Mohannad
    Machine learning has permeated every part of our data lives. With the prevalence of machine learning comes an insatiable need for data, including sensitive personal data. As a result, the need arose to develop techniques for machine learning tasks that preserve individual privacy while providing high utility by learning from private data somehow. An important class of machine learning tasks is clustering, which can potentially be used to study diseases by identifying clusters of patients. As patient information is private, private clustering algorithms would help us infer patterns among patients while protecting their data. DBSCAN is a clustering algorithm that is widely used to detect clusters of arbitrary shape among the data points. Existing private implementations of DBSCAN either exhibit significant leakage, are highly sequential, or are asymptotically inefficient both in runtime and communication cost. In this thesis, we present an efficient approximation of DBSCAN that takes O(log²n) parallel time and O(nlog²n) total work, breaking the quadratic barrier in Secure Multiparty implementations of DBSCAN algorithms and reducing the communication rounds asymptotically from O(n²) to O(log²n).
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    The role of environmental gradients in the shift of wood traits from seedlings to adult trees
    (University of Waterloo, 2026-07-07) Hickey, Hanna
    Tree development, or ontogeny, involves concurrent changes in plant size and environmental conditions, both of which can influence wood structure and function. Disentangling the relative roles of intrinsic (height) and extrinsic (environment) drivers of wood trait variation remains a major challenge. This is important because wood underpins hydraulic efficiency, hydraulic safety, and mechanical support—functions critical for whole-tree performance. In this study, I sampled twigs at a fixed distance from the apex from sugar maple (Acer saccharum) and yellow birch (Betula alleghaniensis) to quantify how wood traits, light availability, and water availability change across seedling, sapling, and adult developmental stages. Across both species, wood structure shifted toward greater hydraulic safety with ontogeny, demonstrated through decreased vessel diameter (Dh), increased vessel number (VN), and increased vessel reinforcement ((t/b)²) in adult trees. Despite shifts towards greater hydraulic safety, hydraulic efficiency (Ks) was maintained across developmental stages, indicating that increases in VN and lumen fraction (F) compensated for reductions in efficiency typically associated with smaller Dh. Wood trait covariation was structured by a hydraulic efficiency–safety trade-off, however traits such as F varied more independently, enabling compensations such that this trade-off did not constrain tissue-level hydraulic function. Contrary to expectations, I did not detect differences in water availability across developmental stages. Although light availability increased from seedlings to adults, it did not explain changes in wood traits with ontogeny. Instead, tree height emerged as the dominant driver of trait values, reflecting increasing hydraulic constraints associated with longer water transport distance. The shift toward smaller Dh and maintained Ks in adult apices contrasts with expectations of increasing transport efficiency in taller trees but is consistent with selection for resistance to freeze–thaw embolism in temperate environments.