Incentivizing Exploration with Heterogeneous Value of Money

Recently, Frazier et al. proposed a natural model for crowdsourced exploration of different a priori unknown options: a principal is interested in the long-term welfare of a population of agents who arrive one by one in a multi-armed bandit setting. However, each agent is myopic, so in order to incentivize him to explore options with better long-term prospects, the principal must offer the agent money. Frazier et al. showed that a simple class of policies called time-expanded are optimal in the worst case, and characterized their budget-reward tradeoff. The previous work assumed that all agents are equally and uniformly susceptible to financial incentives. In reality, agents may have different utility for money. We therefore extend the model of Frazier et al. to allow agents that have heterogeneous and non-linear utilities for money. The principal is informed of the agent's tradeoff via a signal that could be more or less informative. Our main result is to show that a convex program can be used to derive a signal-dependent time-expanded policy which achieves the best possible Lagrangian reward in the worst case. The worst-case guarantee is matched by so-called "Diamonds in the Rough" instances; the proof that the guarantees match is based on showing that two different convex programs have the same optimal solution for these specific instances. These results also extend to the budgeted case as in Frazier et al. We also show that the optimal policy is monotone with respect to information, i.e., the approximation ratio of the optimal policy improves as the signals become more informative.Comment: WINE 201

Learning Adaptive Display Exposure for Real-Time Advertising

In E-commerce advertising, where product recommendations and product ads are presented to users simultaneously, the traditional setting is to display ads at fixed positions. However, under such a setting, the advertising system loses the flexibility to control the number and positions of ads, resulting in sub-optimal platform revenue and user experience. Consequently, major e-commerce platforms (e.g., Taobao.com) have begun to consider more flexible ways to display ads. In this paper, we investigate the problem of advertising with adaptive exposure: can we dynamically determine the number and positions of ads for each user visit under certain business constraints so that the platform revenue can be increased? More specifically, we consider two types of constraints: request-level constraint ensures user experience for each user visit, and platform-level constraint controls the overall platform monetization rate. We model this problem as a Constrained Markov Decision Process with per-state constraint (psCMDP) and propose a constrained two-level reinforcement learning approach to decompose the original problem into two relatively independent sub-problems. To accelerate policy learning, we also devise a constrained hindsight experience replay mechanism. Experimental evaluations on industry-scale real-world datasets demonstrate the merits of our approach in both obtaining higher revenue under the constraints and the effectiveness of the constrained hindsight experience replay mechanism.Comment: accepted by CIKM201

Budgeted Reinforcement Learning in Continuous State Space

A Budgeted Markov Decision Process (BMDP) is an extension of a Markov Decision Process to critical applications requiring safety constraints. It relies on a notion of risk implemented in the shape of a cost signal constrained to lie below an - adjustable - threshold. So far, BMDPs could only be solved in the case of finite state spaces with known dynamics. This work extends the state-of-the-art to continuous spaces environments and unknown dynamics. We show that the solution to a BMDP is a fixed point of a novel Budgeted Bellman Optimality operator. This observation allows us to introduce natural extensions of Deep Reinforcement Learning algorithms to address large-scale BMDPs. We validate our approach on two simulated applications: spoken dialogue and autonomous driving.Comment: N. Carrara and E. Leurent have equally contribute

The stochastic goodwill problem

Stochastic control problems related to optimal advertising under uncertainty are considered. In particular, we determine the optimal strategies for the problem of maximizing the utility of goodwill at launch time and minimizing the disutility of a stream of advertising costs that extends until the launch time for some classes of stochastic perturbations of the classical Nerlove-Arrow dynamics. We also consider some generalizations such as problems with constrained budget and with discretionary launching

A Deep Reinforcement Learning Framework for Rebalancing Dockless Bike Sharing Systems

Bike sharing provides an environment-friendly way for traveling and is booming all over the world. Yet, due to the high similarity of user travel patterns, the bike imbalance problem constantly occurs, especially for dockless bike sharing systems, causing significant impact on service quality and company revenue. Thus, it has become a critical task for bike sharing systems to resolve such imbalance efficiently. In this paper, we propose a novel deep reinforcement learning framework for incentivizing users to rebalance such systems. We model the problem as a Markov decision process and take both spatial and temporal features into consideration. We develop a novel deep reinforcement learning algorithm called Hierarchical Reinforcement Pricing (HRP), which builds upon the Deep Deterministic Policy Gradient algorithm. Different from existing methods that often ignore spatial information and rely heavily on accurate prediction, HRP captures both spatial and temporal dependencies using a divide-and-conquer structure with an embedded localized module. We conduct extensive experiments to evaluate HRP, based on a dataset from Mobike, a major Chinese dockless bike sharing company. Results show that HRP performs close to the 24-timeslot look-ahead optimization, and outperforms state-of-the-art methods in both service level and bike distribution. It also transfers well when applied to unseen areas

Markov Decision Processes with Applications in Wireless Sensor Networks: A Survey

Wireless sensor networks (WSNs) consist of autonomous and resource-limited devices. The devices cooperate to monitor one or more physical phenomena within an area of interest. WSNs operate as stochastic systems because of randomness in the monitored environments. For long service time and low maintenance cost, WSNs require adaptive and robust methods to address data exchange, topology formulation, resource and power optimization, sensing coverage and object detection, and security challenges. In these problems, sensor nodes are to make optimized decisions from a set of accessible strategies to achieve design goals. This survey reviews numerous applications of the Markov decision process (MDP) framework, a powerful decision-making tool to develop adaptive algorithms and protocols for WSNs. Furthermore, various solution methods are discussed and compared to serve as a guide for using MDPs in WSNs

Task-Based Information Compression for Multi-Agent Communication Problems with Channel Rate Constraints

A collaborative task is assigned to a multiagent system (MAS) in which agents are allowed to communicate. The MAS runs over an underlying Markov decision process and its task is to maximize the averaged sum of discounted one-stage rewards. Although knowing the global state of the environment is necessary for the optimal action selection of the MAS, agents are limited to individual observations. The inter-agent communication can tackle the issue of local observability, however, the limited rate of the inter-agent communication prevents the agent from acquiring the precise global state information. To overcome this challenge, agents need to communicate their observations in a compact way such that the MAS compromises the minimum possible sum of rewards. We show that this problem is equivalent to a form of rate-distortion problem which we call the task-based information compression. We introduce a scheme for task-based information compression titled State aggregation for information compression (SAIC), for which a state aggregation algorithm is analytically designed. The SAIC is shown to be capable of achieving near-optimal performance in terms of the achieved sum of discounted rewards. The proposed algorithm is applied to a rendezvous problem and its performance is compared with several benchmarks. Numerical experiments confirm the superiority of the proposed algorithm.Comment: 13 pages, 9 figure