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Register a new userCombinatorial Bandits for Incentivizing Agents with Dynamic Preferences
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Tanner Fiez
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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The design of personalized incentives or recommendations to improve user engagement is gaining prominence as digital platform providers continually emerge. We propose a multi-armed bandit framework for matching incentives to users, whose preferences are unknown a priori and evolving dynamically in time, in a resource constrained environment. We design an algorithm that combines ideas from three distinct domains: (i) a greedy matching paradigm, (ii) the upper confidence bound algorithm (UCB) for bandits, and (iii) mixing times from the theory of Markov chains. For this algorithm, we provide theoretical bounds on the regret and demonstrate its performance via both synthetic and realistic (matching supply and demand in a bike-sharing platform) examples.
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Contextual bandits provide an effective way to model the dynamic data problem in ML by leveraging online (incremental) learning to continuously adjust the predictions based on changing environment. We explore details on contextual bandits, an extension to the traditional reinforcement learning (RL) problem and build a novel algorithm to solve this problem using an array of action-based learners. We apply this approach to model an article recommendation system using an array of stochastic gradient descent (SGD) learners to make predictions on rewards based on actions taken. We then extend the approach to a publicly available MovieLens dataset and explore the findings. First, we make available a simplified simulated dataset showing varying user preferences over time and how this can be evaluated with static and dynamic learning algorithms. This dataset made available as part of this research is intentionally simulated with limited number of features and can be used to evaluate different problem-solving strategies. We will build a classifier using static dataset and evaluate its performance on this dataset. We show limitations of static learner due to fixed context at a point of time and how changing that context brings down the accuracy. Next we develop a novel algorithm for solving the contextual bandit problem. Similar to the linear bandits, this algorithm maps the reward as a function of context vector but uses an array of learners to capture variation between actions/arms. We develop a bandit algorithm using an array of stochastic gradient descent (SGD) learners, with separate learner per arm. Finally, we will apply this contextual bandit algorithm to predicting movie ratings over time by different users from the standard Movie Lens dataset and demonstrate the results.
We unify two prominent lines of work on multi-armed bandits: bandits with knapsacks (BwK) and combinatorial semi-bandits. The former concerns limited resources consumed by the algorithm, e.g., limited supply in dynamic pricing. The latter allows a huge number of actions but assumes combinatorial structure and additional feedback to make the problem tractable. We define a common generalization, support it with several motivating examples, and design an algorithm for it. Our regret bounds are comparable with those for BwK and combinatorial semi- bandits.
A stochastic combinatorial semi-bandit is an online learning problem where at each step a learning agent chooses a subset of ground items subject to combinatorial constraints, and then observes stochastic weights of these items and receives their sum as a payoff. In this paper, we consider efficient learning in large-scale combinatorial semi-bandits with linear generalization, and as a solution, propose two learning algorithms called Combinatorial Linear Thompson Sampling (CombLinTS) and Combinatorial Linear UCB (CombLinUCB). Both algorithms are computationally efficient as long as the offline version of the combinatorial problem can be solved efficiently. We establish that CombLinTS and CombLinUCB are also provably statistically efficient under reasonable assumptions, by developing regret bounds that are independent of the problem scale (number of items) and sublinear in time. We also evaluate CombLinTS on a variety of problems with thousands of items. Our experiment results demonstrate that CombLinTS is scalable, robust to the choice of algorithm parameters, and significantly outperforms the best of our baselines.
We consider the stochastic combinatorial semi-bandit problem with adversarial corruptions. We provide a simple combinatorial algorithm that can achieve a regret of $tilde{O}left(C+d^2K/Delta_{min}right)$ where $C$ is the total amount of corruptions, $d$ is the maximal number of arms one can play in each round, $K$ is the number of arms. If one selects only one arm in each round, we achieves a regret of $tilde{O}left(C+sum_{Delta_i>0}(1/Delta_i)right)$. Our algorithm is combinatorial and improves on the previous combinatorial algorithm by [Gupta et al., COLT2019] (their bound is $tilde{O}left(KC+sum_{Delta_i>0}(1/Delta_i)right)$), and almost matches the best known bounds obtained by [Zimmert et al., ICML2019] and [Zimmert and Seldin, AISTATS2019] (up to logarithmic factor). Note that the algorithms in [Zimmert et al., ICML2019] and [Zimmert and Seldin, AISTATS2019] require one to solve complex convex programs while our algorithm is combinatorial, very easy to implement, requires weaker assumptions and has very low oracle complexity and running time. We also study the setting where we only get access to an approximation oracle for the stochastic combinatorial semi-bandit problem. Our algorithm achieves an (approximation) regret bound of $tilde{O}left(dsqrt{KT}right)$. Our algorithm is very simple, only worse than the best known regret bound by $sqrt{d}$, and has much lower oracle complexity than previous work.
We study the problem of incentivizing exploration for myopic users in linear bandits, where the users tend to exploit arm with the highest predicted reward instead of exploring. In order to maximize the long-term reward, the system offers compensation to incentivize the users to pull the exploratory arms, with the goal of balancing the trade-off among exploitation, exploration and compensation. We consider a new and practically motivated setting where the context features observed by the user are more informative than those used by the system, e.g., features based on users private information are not accessible by the system. We propose a new method to incentivize exploration under such information gap, and prove that the method achieves both sublinear regret and sublinear compensation. We theoretical and empirically analyze the added compensation due to the information gap, compared with the case that the system has access to the same context features as the user, i.e., without information gap. We also provide a compensation lower bound of our problem.
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