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Register a new userContextual Recommendations and Low-Regret Cutting-Plane Algorithms
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Added by
Jonathan Schneider
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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We consider the following variant of contextual linear bandits motivated by routing applications in navigational engines and recommendation systems. We wish to learn a hidden $d$-dimensional value $w^*$. Every round, we are presented with a subset $mathcal{X}_t subseteq mathbb{R}^d$ of possible actions. If we choose (i.e. recommend to the user) action $x_t$, we obtain utility $langle x_t, w^* rangle$ but only learn the identity of the best action $argmax_{x in mathcal{X}_t} langle x, w^* rangle$. We design algorithms for this problem which achieve regret $O(dlog T)$ and $exp(O(d log d))$. To accomplish this, we design novel cutting-plane algorithms with low regret -- the total distance between the true point $w^*$ and the hyperplanes the separation oracle returns. We also consider the variant where we are allowed to provide a list of several recommendations. In this variant, we give an algorithm with $O(d^2 log d)$ regret and list size $mathrm{poly}(d)$. Finally, we construct nearly tight algorithms for a weaker variant of this problem where the learner only learns the identity of an action that is better than the recommendation. Our results rely on new algorithmic techniques in convex geometry (including a variant of Steiners formula for the centroid of a convex set) which may be of independent interest.
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Decision making is a challenging task in online recommender systems. The decision maker often needs to choose a contextual item at each step from a set of candidates. Contextual bandit algorithms have been successfully deployed to such applications, for the trade-off between exploration and exploitation and the state-of-art performance on minimizing online costs. However, the applicability of existing contextual bandit methods is limited by the over-simplified assumptions of the problem, such as assuming a simple form of the reward function or assuming a static environment where the states are not affected by previous actions. In this work, we put forward Policy Gradients for Contextual Recommendations (PGCR) to solve the problem without those unrealistic assumptions. It optimizes over a restricted class of policies where the marginal probability of choosing an item (in expectation of other items) has a simple closed form, and the gradient of the expected return over the policy in this class is in a succinct form. Moreover, PGCR leverages two useful heuristic techniques called Time-Dependent Greed and Actor-Dropout. The former ensures PGCR to be empirically greedy in the limit, and the latter addresses the trade-off between exploration and exploitation by using the policy network with Dropout as a Bayesian approximation. PGCR can solve the standard contextual bandits as well as its Markov Decision Process generalization. Therefore it can be applied to a wide range of realistic settings of recommendations, such as personalized advertising. We evaluate PGCR on toy datasets as well as a real-world dataset of personalized music recommendations. Experiments show that PGCR enables fast convergence and low regret, and outperforms both classic contextual-bandits and vanilla policy gradient methods.
We introduce the online stochastic Convex Programming (CP) problem, a very general version of stochastic online problems which allows arbitrary concave objectives and convex feasibility constraints. Many well-studied problems like online stochastic packing and covering, online stochastic matching with concave returns, etc. form a special case of online stochastic CP. We present fast algorithms for these problems, which achieve near-optimal regret guarantees for both the i.i.d. and the random permutation models of stochastic inputs. When applied to the special case online packing, our ideas yield a simpler and faster primal-dual algorithm for this well studied problem, which achieves the optimal competitive ratio. Our techniques make explicit the connection of primal-dual paradigm and online learning to online stochastic CP.
We study contextual bandits with ancillary constraints on resources, which are common in real-world applications such as choosing ads or dynamic pricing of items. We design the first algorithm for solving these problems that handles constrained resources other than time, and improves over a trivial reduction to the non-contextual case. We consider very general settings for both contextual bandits (arbitrary policy sets, e.g. Dudik et al. (UAI11)) and bandits with resource constraints (bandits with knapsacks, Badanidiyuru et al. (FOCS13)), and prove a regret guarantee with near-optimal statistical properties.
We consider two robu
A dominant approach to solving large imperfect-information games is Counterfactural Regret Minimization (CFR). In CFR, many regret minimization problems are combined to solve the game. For very large games, abstraction is typically needed to render CFR tractable. Abstractions are often manually tuned, possibly removing important strategic differences in the full game and harming performance. Function approximation provides a natural solution to finding good abstractions to approximate the full game. A common approach to incorporating function approximation is to learn the inputs needed for a regret minimizing algorithm, allowing for generalization across many regret minimization problems. This paper gives regret bounds when a regret minimizing algorithm uses estimates instead of true values. This form of analysis is the first to generalize to a larger class of $(Phi, f)$-regret matching algorithms, and includes different forms of regret such as swap, internal, and external regret. We demonstrate how these results give a slightly tighter bound for Regression Regret-Matching (RRM), and present a novel bound for combining regression with Hedge.
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