Learning Linear Dynamics from Bilinear Observations

We consider the problem of learning a realization of a partially observed dynamical system with linear state transitions and bilinear observations. Under very mild assumptions on the process and measurement noises, we provide a finite time analysis for learning the unknown dynamics matrices (up to a similarity transform). Our analysis involves a regression problem with heavy-tailed and dependent data. Moreover, each row of our design matrix contains a Kronecker product of current input with a history of inputs, making it difficult to guarantee persistence of excitation. We overcome these challenges, first providing a data-dependent high probability error bound for arbitrary but fixed inputs. Then, we derive a data-independent error bound for inputs chosen according to a simple random design. Our main results provide an upper bound on the statistical error rates and sample complexity of learning the unknown dynamics matrices from a single finite trajectory of bilinear observations.

Harm Mitigation in Recommender Systems under User Preference Dynamics

We consider a recommender system that takes into account the interplay between recommendations, the evolution of user interests, and harmful content. We model the impact of recommendations on user behavior, particularly the tendency to consume harmful content. We seek recommendation policies that establish a tradeoff between maximizing click-through rate (CTR) and mitigating harm. We establish conditions under which the user profile dynamics have a stationary point, and propose algorithms for finding an optimal recommendation policy at stationarity. We experiment on a semi-synthetic movie recommendation setting initialized with real data and observe that our policies outperform baselines at simultaneously maximizing CTR and mitigating harm.

Random Features Approximation for Control-Affine Systems

Modern data-driven control applications call for flexible nonlinear models that are amenable to principled controller synthesis and realtime feedback. Many nonlinear dynamical systems of interest are control affine. We propose two novel classes of nonlinear feature representations which capture control affine structure while allowing for arbitrary complexity in the state dependence. Our methods make use of random features (RF) approximations, inheriting the expressiveness of kernel methods at a lower computational cost. We formalize the representational capabilities of our methods by showing their relationship to the Affine Dot Product (ADP) kernel proposed by Casta\~neda et al. (2021) and a novel Affine Dense (AD) kernel that we introduce. We further illustrate the utility by presenting a case study of data-driven optimization-based control using control certificate functions (CCF). Simulation experiments on a double pendulum empirically demonstrate the advantages of our methods.

Learning from Streaming Data when Users Choose

In digital markets comprised of many competing services, each user chooses between multiple service providers according to their preferences, and the chosen service makes use of the user data to incrementally improve its model. The service providers' models influence which service the user will choose at the next time step, and the user's choice, in return, influences the model update, leading to a feedback loop. In this paper, we formalize the above dynamics and develop a simple and efficient decentralized algorithm to locally minimize the overall user loss. Theoretically, we show that our algorithm asymptotically converges to stationary points of of the overall loss almost surely. We also experimentally demonstrate the utility of our algorithm with real world data.

To Ask or Not To Ask: Human-in-the-loop Contextual Bandits with Applications in Robot-Assisted Feeding

Robot-assisted bite acquisition involves picking up food items that vary in their shape, compliance, size, and texture. A fully autonomous strategy for bite acquisition is unlikely to efficiently generalize to this wide variety of food items. We propose to leverage the presence of the care recipient to provide feedback when the system encounters novel food items. However, repeatedly asking for help imposes cognitive workload on the user. In this work, we formulate human-in-the-loop bite acquisition within a contextual bandit framework and propose a novel method, LinUCB-QG, that selectively asks for help. This method leverages a predictive model of cognitive workload in response to different types and timings of queries, learned using data from 89 participants collected in an online user study. We demonstrate that this method enhances the balance between task performance and cognitive workload compared to autonomous and querying baselines, through experiments in a food dataset-based simulator and a user study with 18 participants without mobility limitations.

Accounting for AI and Users Shaping One Another: The Role of Mathematical Models

As AI systems enter into a growing number of societal domains, these systems increasingly shape and are shaped by user preferences, opinions, and behaviors. However, the design of AI systems rarely accounts for how AI and users shape one another. In this position paper, we argue for the development of formal interaction models which mathematically specify how AI and users shape one another. Formal interaction models can be leveraged to (1) specify interactions for implementation, (2) monitor interactions through empirical analysis, (3) anticipate societal impacts via counterfactual analysis, and (4) control societal impacts via interventions. The design space of formal interaction models is vast, and model design requires careful consideration of factors such as style, granularity, mathematical complexity, and measurability. Using content recommender systems as a case study, we critically examine the nascent literature of formal interaction models with respect to these use-cases and design axes. More broadly, we call for the community to leverage formal interaction models when designing, evaluating, or auditing any AI system which interacts with users.

Strategic Usage in a Multi-Learner Setting

Real-world systems often involve some pool of users choosing between a set of services. With the increase in popularity of online learning algorithms, these services can now self-optimize, leveraging data collected on users to maximize some reward such as service quality. On the flipside, users may strategically choose which services to use in order to pursue their own reward functions, in the process wielding power over which services can see and use their data. Extensive prior research has been conducted on the effects of strategic users in single-service settings, with strategic behavior manifesting in the manipulation of observable features to achieve a desired classification; however, this can often be costly or unattainable for users and fails to capture the full behavior of multi-service dynamic systems. As such, we analyze a setting in which strategic users choose among several available services in order to pursue positive classifications, while services seek to minimize loss functions on their observations. We focus our analysis on realizable settings, and show that naive retraining can still lead to oscillation even if all users are observed at different times; however, if this retraining uses memory of past observations, convergent behavior can be guaranteed for certain loss function classes. We provide results obtained from synthetic and real-world data to empirically validate our theoretical findings.

Initializing Services in Interactive ML Systems for Diverse Users

This paper studies ML systems that interactively learn from users across multiple subpopulations with heterogeneous data distributions. The primary objective is to provide specialized services for different user groups while also predicting user preferences. Once the users select a service based on how well the service anticipated their preference, the services subsequently adapt and refine themselves based on the user data they accumulate, resulting in an iterative, alternating minimization process between users and services (learning dynamics). Employing such tailored approaches has two main challenges: (i) Unknown user preferences: Typically, data on user preferences are unavailable without interaction, and uniform data collection across a large and diverse user base can be prohibitively expensive. (ii) Suboptimal Local Solutions: The total loss (sum of loss functions across all users and all services) landscape is not convex even if the individual losses on a single service are convex, making it likely for the learning dynamics to get stuck in local minima. The final outcome of the aforementioned learning dynamics is thus strongly influenced by the initial set of services offered to users, and is not guaranteed to be close to the globally optimal outcome. In this work, we propose a randomized algorithm to adaptively select very few users to collect preference data from, while simultaneously initializing a set of services. We prove that under mild assumptions on the loss functions, the expected total loss achieved by the algorithm right after initialization is within a factor of the globally optimal total loss with complete user preference data, and this factor scales only logarithmically in the number of services. Our theory is complemented by experiments on real as well as semi-synthetic datasets.

Ranking with Long-Term Constraints

The feedback that users provide through their choices (e.g., clicks, purchases) is one of the most common types of data readily available for training search and recommendation algorithms. However, myopically training systems based on choice data may only improve short-term engagement, but not the long-term sustainability of the platform and the long-term benefits to its users, content providers, and other stakeholders. In this paper, we thus develop a new framework in which decision makers (e.g., platform operators, regulators, users) can express long-term goals for the behavior of the platform (e.g., fairness, revenue distribution, legal requirements). These goals take the form of exposure or impact targets that go well beyond individual sessions, and we provide new control-based algorithms to achieve these goals. In particular, the controllers are designed to achieve the stated long-term goals with minimum impact on short-term engagement. Beyond the principled theoretical derivation of the controllers, we evaluate the algorithms on both synthetic and real-world data. While all controllers perform well, we find that they provide interesting trade-offs in efficiency, robustness, and the ability to plan ahead.

Decision-aid or Controller? Steering Human Decision Makers with Algorithms

Algorithms are used to aid human decision makers by making predictions and recommending decisions. Currently, these algorithms are trained to optimize prediction accuracy. What if they were optimized to control final decisions? In this paper, we study a decision-aid algorithm that learns about the human decision maker and provides ''personalized recommendations'' to influence final decisions. We first consider fixed human decision functions which map observable features and the algorithm's recommendations to final decisions. We characterize the conditions under which perfect control over final decisions is attainable. Under fairly general assumptions, the parameters of the human decision function can be identified from past interactions between the algorithm and the human decision maker, even when the algorithm was constrained to make truthful recommendations. We then consider a decision maker who is aware of the algorithm's manipulation and responds strategically. By posing the setting as a variation of the cheap talk game [Crawford and Sobel, 1982], we show that all equilibria are partition equilibria where only coarse information is shared: the algorithm recommends an interval containing the ideal decision. We discuss the potential applications of such algorithms and their social implications.