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When an Agent visits a platform recommending a menu of content to selectfrom, their choice of item depends not only on fixed preferences, but also ontheir prior engagements with the platform. The Recommender's primary objectiveis typically to encourage content consumption which optimizes some reward, suchas ad revenue, but they often also aim to ensure that a wide variety of contentis consumed by the Agent over time. We formalize this problem as an adversarialbandit task. At each step, the Recommender presents a menu of $k$ (out of $n$)items to the Agent, who selects one item in the menu according to their unknownpreference model, which maps their history of past items to relative selectionprobabilities. The Recommender then observes the Agent's chosen item andreceives bandit feedback of the item's reward. In addition to optimizing rewardfrom selected items, the Recommender must also ensure that the totaldistribution of chosen items has sufficiently high entropy.  We define a class of preference models which are locally learnable, i.e.behavior over the entire domain can be estimated by only observing behavior ina small region; this includes models representable by bounded-degreepolynomials as well as functions with a sparse Fourier basis. For this class,we give an algorithm for the Recommender which obtains $\tilde{O}(T^{3/4})$regret against all item distributions satisfying two conditions: they aresufficiently diversified, and they are instantaneously realizable at anyhistory by some distribution over menus. We show that these conditions areclosely connected: all sufficiently high-entropy distributions areinstantaneously realizable at any item history. We also give a set of negativeresults justifying our assumptions, in the form of a runtime lower bound fornon-local learning and linear regret lower bounds for alternate benchmarks.

Diversified Recommendations for Agents with Adaptive Preferences