Shiliang Zuo

Shiliang Zuo

I study the problem of learning a Lipschitz function with corrupted binary signals. The learner tries to learn a $L$-Lipschitz function $f: [0,1]^d \rightarrow [0, L]$ that the adversary chooses. There is a total of $T$ rounds. In each round $t$, the adversary selects a context vector $x_t$ in the input space, and the learner makes a guess to the true function value $f(x_t)$ and receives a binary signal indicating whether the guess is high or low. In a total of $C$ rounds, the signal may be corrupted, though the value of $C$ is \emph{unknown} to the learner. The learner's goal is to incur a small cumulative loss. This work introduces the new algorithmic technique \emph{agnostic checking} as well as new analysis techniques. I design algorithms which: for the symmetric loss, the learner achieves regret $L\cdot O(C\log T)$ with $d = 1$ and $L\cdot O_d(C\log T + T^{(d-1)/d})$ with $d > 1$; for the pricing loss, the learner achieves regret $L\cdot \widetilde{O} (T^{d/(d+1)} + C\cdot T^{1/(d+1)})$.

Shiliang Zuo

Machine learning has become increasingly popular in informing data-driven policy-making. Policies influence behavior in individuals or populations, and ideally, through observational signals, policy-makers learn which policies are effective. However, in many settings, individual actions cannot be perfectly observed. This issue, known in economics as moral hazard, poses a significant challenge. In this work, we study the foundational multitasking principal-agent contract design problem and demonstrate how instrumental regression and the generalized method of moments (GMM) estimator can be used to estimate or learn a good contract. As a bonus result, we also give a uniformity characterization of the shape of the optimal contract.

Shiliang Zuo

Linear contracts are ubiquitous in practice, yet optimal contract theory often prescribes complex, nonlinear structures. We provide a distributional robustness justification for linear contracts. We study a principal-agent problem where the agent exerts costly effort across multiple tasks, generating a stochastic signal upon which the principal conditions payment. The principal faces distributional ambiguity: she knows the expected signal for each effort level, but not the full distribution. She seeks a contract maximizing her worst-case payoff over all distributions consistent with this partial knowledge. Our main result shows that linear contracts are optimal for such a principal. For any contract, there exists a linear contract achieving weakly higher worst-case payoff. The proof introduces the concavification approach built around the notion of self-inducing actions; these are actions where an affine contract simultaneously induces the action as optimal and supports the concave envelope of payments from above. We show that self-inducing actions always exist as maximizers of the gap between the concave envelope and agent's cost function. We extend these results to multi-party settings. In common agency with multiple principals, we show that affine contracts improve all principals' worst-case payoffs. In team production with multiple agents, we establish a complementary necessity result: if any agent's contract is non-affine, the unique ex-post robust equilibrium is zero effort. Finally, we show that homogeneous utility and cost functions yield tractable characterizations, enabling closed-form approximation ratios and a sharp boundary between computational tractability results.

Shiliang Zuo

We study dynamic pricing where a seller repeatedly interacts with a strategic, non-myopic buyer who has a fixed private valuation and discounts future utility. Prior work focused exclusively on posted-price mechanisms, which only extract binary accept/reject signals. For our first result, we show that menu mechanisms-offering allocation-payment contracts are able to achieve $O(T_γ\log T_γ)$ regret, where $T_γ$ is the buyer's effective discounted time horizon, improving all prior bounds. Our second contribution is more conceptual in nature. The problem of dynamic pricing sits at the intersection of two paradigms: adaptive learning in computer science / machine learning and revelation-principle-based mechanism design in economics-yet their relationship has remained unclear. We establish a fundamental equivalence: indirect learning mechanisms and direct revelation mechanisms achieve identical optimal regret. The adaptive, data-driven algorithms of online learning and explicit type elicitation are two languages towards solving the same problem; hence, learning is revelation in disguise.

Rohan Deb, Yikun Ban, Shiliang Zuo et al.

Recent works have shown a reduction from contextual bandits to online regression under a realizability assumption [Foster and Rakhlin, 2020, Foster and Krishnamurthy, 2021]. In this work, we investigate the use of neural networks for such online regression and associated Neural Contextual Bandits (NeuCBs). Using existing results for wide networks, one can readily show a ${\mathcal{O}}(\sqrt{T})$ regret for online regression with square loss, which via the reduction implies a ${\mathcal{O}}(\sqrt{K} T^{3/4})$ regret for NeuCBs. Departing from this standard approach, we first show a $\mathcal{O}(\log T)$ regret for online regression with almost convex losses that satisfy QG (Quadratic Growth) condition, a generalization of the PL (Polyak-Łojasiewicz) condition, and that have a unique minima. Although not directly applicable to wide networks since they do not have unique minima, we show that adding a suitable small random perturbation to the network predictions surprisingly makes the loss satisfy QG with unique minima. Based on such a perturbed prediction, we show a ${\mathcal{O}}(\log T)$ regret for online regression with both squared loss and KL loss, and subsequently convert these respectively to $\tilde{\mathcal{O}}(\sqrt{KT})$ and $\tilde{\mathcal{O}}(\sqrt{KL^*} + K)$ regret for NeuCB, where $L^*$ is the loss of the best policy. Separately, we also show that existing regret bounds for NeuCBs are $Ω(T)$ or assume i.i.d. contexts, unlike this work. Finally, our experimental results on various datasets demonstrate that our algorithms, especially the one based on KL loss, persistently outperform existing algorithms.

Shiliang Zuo

This work studies the online contract design problem. The principal's goal is to learn the optimal contract that maximizes her utility through repeated interactions, without prior knowledge of the agent's type (i.e., the agent's cost and production functions). We leverage the structure provided by continuous action spaces, which allows the application of first-order conditions (FOC) to characterize the agent's behavior. In some cases, we utilize conditions from the first-order approach (FOA) in economics, but in certain settings, we are able to apply FOC without additional assumptions, leading to simpler and more principled algorithms. We illustrate this approach in three problem settings. Firstly, we study the problem of learning the optimal contract when there can be many outcomes. In contrast to prior works that design highly specialized algorithms, we show that the problem can be directly reduced to Lipschitz bandits. Secondly, we study the problem of learning linear contracts. While the contracting problem involves hidden action (moral hazard) and the pricing problem involves hidden value (adverse selection), the two problems share a similar optimization structure, which enables direct reduction between the problem of learning linear contracts and dynamic pricing. Thirdly, we study the problem of learning contracts with many outcomes when agents are identical and provide an algorithm with polynomial sample complexity.

Aleksandrs Slivkins, Yunzong Xu, Shiliang Zuo

We study the greedy (exploitation-only) algorithm in bandit problems with a known reward structure. We allow arbitrary finite reward structures, while prior work focused on a few specific ones. We fully characterize when the greedy algorithm asymptotically succeeds or fails, in the sense of sublinear vs. linear regret as a function of time. Our characterization identifies a partial identifiability property of the problem instance as the necessary and sufficient condition for the asymptotic success. Notably, once this property holds, the problem becomes easy -- any algorithm will succeed (in the same sense as above), provided it satisfies a mild non-degeneracy condition. Our characterization extends to contextual bandits and interactive decision-making with arbitrary feedback. Examples demonstrating broad applicability and extensions to infinite reward structures are provided.

Zhuolin Yang, Linyi Li, Xiaojun Xu et al.

Adversarial Transferability is an intriguing property - adversarial perturbation crafted against one model is also effective against another model, while these models are from different model families or training processes. To better protect ML systems against adversarial attacks, several questions are raised: what are the sufficient conditions for adversarial transferability and how to bound it? Is there a way to reduce the adversarial transferability in order to improve the robustness of an ensemble ML model? To answer these questions, in this work we first theoretically analyze and outline sufficient conditions for adversarial transferability between models; then propose a practical algorithm to reduce the transferability between base models within an ensemble to improve its robustness. Our theoretical analysis shows that only promoting the orthogonality between gradients of base models is not enough to ensure low transferability; in the meantime, the model smoothness is an important factor to control the transferability. We also provide the lower and upper bounds of adversarial transferability under certain conditions. Inspired by our theoretical analysis, we propose an effective Transferability Reduced Smooth(TRS) ensemble training strategy to train a robust ensemble with low transferability by enforcing both gradient orthogonality and model smoothness between base models. We conduct extensive experiments on TRS and compare with 6 state-of-the-art ensemble baselines against 8 whitebox attacks on different datasets, demonstrating that the proposed TRS outperforms all baselines significantly.

Shiliang Zuo

I study adversarial attacks against stochastic bandit algorithms. At each round, the learner chooses an arm, and a stochastic reward is generated. The adversary strategically adds corruption to the reward, and the learner is only able to observe the corrupted reward at each round. Two sets of results are presented in this paper. The first set studies the optimal attack strategies for the adversary. The adversary has a target arm he wishes to promote, and his goal is to manipulate the learner into choosing this target arm $T - o(T)$ times. I design attack strategies against UCB and Thompson Sampling that only spend $\widehat{O}(\sqrt{\log T})$ cost. Matching lower bounds are presented, and the vulnerability of UCB, Thompson sampling, and $\varepsilon$-greedy are exactly characterized. The second set studies how the learner can defend against the adversary. Inspired by literature on smoothed analysis and behavioral economics, I present two simple algorithms that achieve a competitive ratio arbitrarily close to 1.

Shiliang Zuo

Gradient descent is a popular algorithm in optimization, and its performance in convex settings is mostly well understood. In non-convex settings, it has been shown that gradient descent is able to escape saddle points asymptotically and converge to local minimizers [Lee et. al. 2016]. Recent studies also show a perturbed version of gradient descent is enough to escape saddle points efficiently [Jin et. al. 2015, Ge et. al. 2017]. In this paper we show a negative result: gradient descent may take exponential time to escape saddle points, with non-pathological two dimensional functions. While our focus is theoretical, we also conduct experiments verifying our theoretical result. Through our analysis we demonstrate that stochasticity is essential to escape saddle points efficiently.