Data-Driven Goal Recognition Design for General Behavioral Agents

Goal recognition design aims to make limited modifications to decision-making environments with the goal of making it easier to infer the goals of agents acting within those environments. Although various research efforts have been made in goal recognition design, existing approaches are computationally demanding and often assume that agents are (near-)optimal in their decision-making. To address these limitations, we introduce a data-driven approach to goal recognition design that can account for agents with general behavioral models. Following existing literature, we use worst-case distinctiveness ($\textit{wcd}$) as a measure of the difficulty in inferring the goal of an agent in a decision-making environment. Our approach begins by training a machine learning model to predict the $\textit{wcd}$ for a given environment and the agent behavior model. We then propose a gradient-based optimization framework that accommodates various constraints to optimize decision-making environments for enhanced goal recognition. Through extensive simulations, we demonstrate that our approach outperforms existing methods in reducing $\textit{wcd}$ and enhancing runtime efficiency in conventional setups, and it also adapts to scenarios not previously covered in the literature, such as those involving flexible budget constraints, more complex environments, and suboptimal agent behavior. Moreover, we have conducted human-subject experiments which confirm that our method can create environments that facilitate efficient goal recognition from real-world human decision-makers.

Performative Prediction with Bandit Feedback: Learning through Reparameterization

Performative prediction, as introduced by Perdomo et al. (2020), is a framework for studying social prediction in which the data distribution itself changes in response to the deployment of a model. Existing work on optimizing accuracy in this setting hinges on two assumptions that are easily violated in practice: that the performative risk is convex over the deployed model, and that the mapping from the model to the data distribution is known to the model designer in advance. In this paper, we initiate the study of tractable performative prediction problems that do not require these assumptions. To tackle this more challenging setting, we develop a two-level zeroth-order optimization algorithm, where one level aims to compute the distribution map, and the other level reparameterizes the performative prediction objective as a function of the induced data distribution. Under mild conditions, this reparameterization allows us to transform the non-convex objective into a convex one and achieve provable regret guarantees. In particular, we provide a regret bound that is sublinear in the total number of performative samples taken and only polynomial in the dimension of the model parameter.

Optimal Query Complexity of Secure Stochastic Convex Optimization

We study the secure stochastic convex optimization problem. A learner aims to learn the optimal point of a convex function through sequentially querying a (stochastic) gradient oracle. In the meantime, there exists an adversary who aims to free-ride and infer the learning outcome of the learner from observing the learner's queries. The adversary observes only the points of the queries but not the feedback from the oracle. The goal of the learner is to optimize the accuracy, i.e., obtaining an accurate estimate of the optimal point, while securing her privacy, i.e., making it difficult for the adversary to infer the optimal point. We formally quantify this tradeoff between learner's accuracy and privacy and characterize the lower and upper bounds on the learner's query complexity as a function of desired levels of accuracy and privacy. For the analysis of lower bounds, we provide a general template based on information theoretical analysis and then tailor the template to several families of problems, including stochastic convex optimization and (noisy) binary search. We also present a generic secure learning protocol that achieves the matching upper bound up to logarithmic factors.

Fair Bandit Learning with Delayed Impact of Actions

Algorithmic fairness has been studied mostly in a static setting where the implicit assumptions are that the frequencies of historically made decisions do not impact the problem structure in subsequent future. However, for example, the capability to pay back a loan for people in a certain group might depend on historically how frequently that group has been approved loan applications. If banks keep rejecting loan applications to people in a disadvantaged group, it could create a feedback loop and further damage the chance of getting loans for people in that group. This challenge has been noted in several recent works but is under-explored in a more generic sequential learning setting. In this paper, we formulate this delayed and long-term impact of actions within the context of multi-armed bandits (MAB). We generalize the classical bandit setting to encode the dependency of this action "bias" due to the history of the learning. Our goal is to learn to maximize the collected utilities over time while satisfying fairness constraints imposed over arms' utilities, which again depend on the decision they have received. We propose an algorithm that achieves a regret of $\tilde{\mathcal{O}}(KT^{2/3})$ and show a matching regret lower bound of $\Omega(KT^{2/3})$, where $K$ is the number of arms and $T$ denotes the learning horizon. Our results complement the bandit literature by adding techniques to deal with actions with long-term impacts and have implications in designing fair algorithms.

Adaptive Contract Design for Crowdsourcing Markets: Bandit Algorithms for Repeated Principal-Agent Problems

Crowdsourcing markets have emerged as a popular platform for matching available workers with tasks to complete. The payment for a particular task is typically set by the task's requester, and may be adjusted based on the quality of the completed work, for example, through the use of "bonus" payments. In this paper, we study the requester's problem of dynamically adjusting quality-contingent payments for tasks. We consider a multi-round version of the well-known principal-agent model, whereby in each round a worker makes a strategic choice of the effort level which is not directly observable by the requester. In particular, our formulation significantly generalizes the budget-free online task pricing problems studied in prior work. We treat this problem as a multi-armed bandit problem, with each "arm" representing a potential contract. To cope with the large (and in fact, infinite) number of arms, we propose a new algorithm, AgnosticZooming, which discretizes the contract space into a finite number of regions, effectively treating each region as a single arm. This discretization is adaptively refined, so that more promising regions of the contract space are eventually discretized more finely. We analyze this algorithm, showing that it achieves regret sublinear in the time horizon and substantially improves over non-adaptive discretization (which is the only competing approach in the literature). Our results advance the state of art on several different topics: the theory of crowdsourcing markets, principal-agent problems, multi-armed bandits, and dynamic pricing.

Low-Cost Learning via Active Data Procurement

We design mechanisms for online procurement of data held by strategic agents for machine learning tasks. The challenge is to use past data to actively price future data and give learning guarantees even when an agent's cost for revealing her data may depend arbitrarily on the data itself. We achieve this goal by showing how to convert a large class of no-regret algorithms into online posted-price and learning mechanisms. Our results in a sense parallel classic sample complexity guarantees, but with the key resource being money rather than quantity of data: With a budget constraint $B$, we give robust risk (predictive error) bounds on the order of $1/\sqrt{B}$. Because we use an active approach, we can often guarantee to do significantly better by leveraging correlations between costs and data. Our algorithms and analysis go through a model of no-regret learning with $T$ arriving pairs (cost, data) and a budget constraint of $B$. Our regret bounds for this model are on the order of $T/\sqrt{B}$ and we give lower bounds on the same order.