Transfer Learning for Contextual Multi-armed Bandits

Motivated by a range of applications, we study in this paper the problem of transfer learning for nonparametric contextual multi-armed bandits under the covariate shift model, where we have data collected on source bandits before the start of the target bandit learning. The minimax rate of convergence for the cumulative regret is established and a novel transfer learning algorithm that attains the minimax regret is proposed. The results quantify the contribution of the data from the source domains for learning in the target domain in the context of nonparametric contextual multi-armed bandits. In view of the general impossibility of adaptation to unknown smoothness, we develop a data-driven algorithm that achieves near-optimal statistical guarantees (up to a logarithmic factor) while automatically adapting to the unknown parameters over a large collection of parameter spaces under an additional self-similarity assumption. A simulation study is carried out to illustrate the benefits of utilizing the data from the auxiliary source domains for learning in the target domain

Optimal treatment allocations in space and time for on-line control of an emerging infectious disease

A key component in controlling the spread of an epidemic is deciding where, whenand to whom to apply an intervention.We develop a framework for using data to informthese decisionsin realtime.We formalize a treatment allocation strategy as a sequence of functions, oneper treatment period, that map up-to-date information on the spread of an infectious diseaseto a subset of locations where treatment should be allocated. An optimal allocation strategyoptimizes some cumulative outcome, e.g. the number of uninfected locations, the geographicfootprint of the disease or the cost of the epidemic. Estimation of an optimal allocation strategyfor an emerging infectious disease is challenging because spatial proximity induces interferencebetween locations, the number of possible allocations is exponential in the number oflocations, and because disease dynamics and intervention effectiveness are unknown at outbreak.We derive a Bayesian on-line estimator of the optimal allocation strategy that combinessimulation–optimization with Thompson sampling.The estimator proposed performs favourablyin simulation experiments. This work is motivated by and illustrated using data on the spread ofwhite nose syndrome, which is a highly fatal infectious disease devastating bat populations inNorth America

Nearest Neighbour with Bandit Feedback

In this paper we adapt the nearest neighbour rule to the contextual bandit problem. Our algorithm handles the fully adversarial setting in which no assumptions at all are made about the data-generation process. When combined with a sufficiently fast data-structure for (perhaps approximate) adaptive nearest neighbour search, such as a navigating net, our algorithm is extremely efficient - having a per trial running time polylogarithmic in both the number of trials and actions, and taking only quasi-linear space

Federated Linear Contextual Bandits with User-level Differential Privacy

This paper studies federated linear contextual bandits under the notion of user-level differential privacy (DP). We first introduce a unified federated bandits framework that can accommodate various definitions of DP in the sequential decision-making setting. We then formally introduce user-level central DP (CDP) and local DP (LDP) in the federated bandits framework, and investigate the fundamental trade-offs between the learning regrets and the corresponding DP guarantees in a federated linear contextual bandits model. For CDP, we propose a federated algorithm termed as \robin and show that it is near-optimal in terms of the number of clients $M$ and the privacy budget $\varepsilon$ by deriving nearly-matching upper and lower regret bounds when user-level DP is satisfied. For LDP, we obtain several lower bounds, indicating that learning under user-level $(\varepsilon,\delta)$-LDP must suffer a regret blow-up factor at least {$\min\{1/\varepsilon,M\}$ or $\min\{1/\sqrt{\varepsilon},\sqrt{M}\}$} under different conditions.Comment: Accepted by ICML 202

Learning how to act: making good decisions with machine learning

This thesis is about machine learning and statistical approaches to decision making. How can we learn from data to anticipate the consequence of, and optimally select, interventions or actions? Problems such as deciding which medication to prescribe to patients, who should be released on bail, and how much to charge for insurance are ubiquitous, and have far reaching impacts on our lives. There are two fundamental approaches to learning how to act: reinforcement learning, in which an agent directly intervenes in a system and learns from the outcome, and observational causal inference, whereby we seek to infer the outcome of an intervention from observing the system. The goal of this thesis to connect and unify these key approaches. I introduce causal bandit problems: a synthesis that combines causal graphical models, which were developed for observational causal inference, with multi-armed bandit problems, which are a subset of reinforcement learning problems that are simple enough to admit formal analysis. I show that knowledge of the causal structure allows us to transfer information learned about the outcome of one action to predict the outcome of an alternate action, yielding a novel form of structure between bandit arms that cannot be exploited by existing algorithms. I propose an algorithm for causal bandit problems and prove bounds on the simple regret demonstrating it is close to mini-max optimal and better than algorithms that do not use the additional causal information

Active and Passive Causal Inference Learning

This paper serves as a starting point for machine learning researchers, engineers and students who are interested in but not yet familiar with causal inference. We start by laying out an important set of assumptions that are collectively needed for causal identification, such as exchangeability, positivity, consistency and the absence of interference. From these assumptions, we build out a set of important causal inference techniques, which we do so by categorizing them into two buckets; active and passive approaches. We describe and discuss randomized controlled trials and bandit-based approaches from the active category. We then describe classical approaches, such as matching and inverse probability weighting, in the passive category, followed by more recent deep learning based algorithms. By finishing the paper with some of the missing aspects of causal inference from this paper, such as collider biases, we expect this paper to provide readers with a diverse set of starting points for further reading and research in causal inference and discovery

Tracking Most Significant Shifts in Nonparametric Contextual Bandits

We study nonparametric contextual bandits where Lipschitz mean reward functions may change over time. We first establish the minimax dynamic regret rate in this less understood setting in terms of number of changes $L$ and total-variation $V$, both capturing all changes in distribution over context space, and argue that state-of-the-art procedures are suboptimal in this setting. Next, we tend to the question of an adaptivity for this setting, i.e. achieving the minimax rate without knowledge of $L$ or $V$. Quite importantly, we posit that the bandit problem, viewed locally at a given context $X_t$, should not be affected by reward changes in other parts of context space $\cal X$. We therefore propose a notion of change, which we term experienced significant shifts, that better accounts for locality, and thus counts considerably less changes than $L$ and $V$. Furthermore, similar to recent work on non-stationary MAB (Suk & Kpotufe, 2022), experienced significant shifts only count the most significant changes in mean rewards, e.g., severe best-arm changes relevant to observed contexts. Our main result is to show that this more tolerant notion of change can in fact be adapted to

Non-stationary Contextual Bandits and Universal Learning

We study the fundamental limits of learning in contextual bandits, where a learner's rewards depend on their actions and a known context, which extends the canonical multi-armed bandit to the case where side-information is available. We are interested in universally consistent algorithms, which achieve sublinear regret compared to any measurable fixed policy, without any function class restriction. For stationary contextual bandits, when the underlying reward mechanism is time-invariant, [Blanchard et al.] characterized learnable context processes for which universal consistency is achievable; and further gave algorithms ensuring universal consistency whenever this is achievable, a property known as optimistic universal consistency. It is well understood, however, that reward mechanisms can evolve over time, possibly depending on the learner's actions. We show that optimistic universal learning for non-stationary contextual bandits is impossible in general, contrary to all previously studied settings in online learning -- including standard supervised learning. We also give necessary and sufficient conditions for universal learning under various non-stationarity models, including online and adversarial reward mechanisms. In particular, the set of learnable processes for non-stationary rewards is still extremely general -- larger than i.i.d., stationary or ergodic -- but in general strictly smaller than that for supervised learning or stationary contextual bandits, shedding light on new non-stationary phenomena