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        "event_title":"Dynamic Contracting: Sequential Payments, Stochastic Target Problems, and State-Constrained Control",
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        "combined_title":"Dynamic Contracting: Sequential Payments, Stochastic Target Problems, and State-Constrained Control: Liwei Huang",
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        "description":"Abstract:\n\nThis thesis develops stochastic-control methods for dynamic principal\u2013agent problems in continuous time. The first part studies adverse selection with moral hazard, where the agent privately observes her type. We reformulate the principal\u2019s problem as an optimal control problem with partial information and state constraints, and characterize the value through state-constrained HJB equations. The second part studies sequential contracting with multiple lump-sum payments at fixed dates, using recursive BSDEs to reduce the Stackelberg problem to a single stochastic control problem with mixed static and continuous controls. The third part allows the principal to choose both the timing and size of discretionary bonuses, leading to a mixed control-stopping problem characterized by HJB variational inequalities. Together, the thesis shows how private information, payment timing, and contractual flexibility shape optimal incentive design.",
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        "event_title":"Learning with Quantum Examples: Multiclass, Online, and Smoothed Settings",
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        "description":"Abstract:\n\nAs quantum computing progresses toward fault-tolerant architectures, the question of which computational tasks admit provable quantum advantages and which do not has become increasingly central. Learning theory, and in particular learning from quantum examples, provides one of the few settings in which unconditional quantum-classical separations can be established. In distribution-free (i.e., worst-case) PAC learning, existing results show that quantum examples provide no asymptotic advantage in sample complexity. In contrast, under the uniform distribution, unbounded quantum-classical separations are known for learning Fourier-sparse Boolean functions. Together, these results reveal a striking dichotomy. However, this understanding has largely been developed in the context of learning Boolean functions in the batch setting, leaving open how these phenomena extend more broadly. This thesis develops the theory of learning with quantum examples beyond the batch Boolean setting along three directions: multiclass learning, online learning, and smoothed learning.\n\nIn the multiclass PAC setting, we establish upper and lower bounds on quantum sample complexity in both the realizable and agnostic regimes, finding that quantum examples continue to yield no distribution-independent separation from classical examples, with learning rates governed by the Natarajan dimension up to logarithmic factors in the label-space size. We next study online learning, where no standard framework for learning with quantum examples existed prior to this work. We provide such a model by lifting the classical online framework to one in which the adversary provides distributions over labeled examples, and then by encoding these distributions as quantum examples. We establish expected regret guarantees for binary and multiclass classification in both the realizable and agnostic settings. The central finding is that unrestricted adversarial power permits highly concentrated distributions that dequantize the learning problem. Motivated by this dequantization phenomenon, we develop a smoothed learning framework that constrains distributions to be smooth, interpolating between the concentrated-distribution regime, in which no quantum advantage exists, and the uniform-distribution regime, in which unbounded separations are known. For the class of Fourier-sparse Boolean functions, we show that such separations persist throughout a nontrivial near-uniform regime in both the batch and online settings.\n\nTogether, these results paint a coherent picture of learning with quantum examples beyond the batch Boolean setting, showing that quantum-classical separations depend on the interplay between hypothesis class structure, distributional assumptions, and the degree of adversarial control permitted in the learning process.",
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