1,549 research outputs found
Exploration vs Exploitation vs Safety: Risk-averse Multi-Armed Bandits
Motivated by applications in energy management, this paper presents the
Multi-Armed Risk-Aware Bandit (MARAB) algorithm. With the goal of limiting the
exploration of risky arms, MARAB takes as arm quality its conditional value at
risk. When the user-supplied risk level goes to 0, the arm quality tends toward
the essential infimum of the arm distribution density, and MARAB tends toward
the MIN multi-armed bandit algorithm, aimed at the arm with maximal minimal
value. As a first contribution, this paper presents a theoretical analysis of
the MIN algorithm under mild assumptions, establishing its robustness
comparatively to UCB. The analysis is supported by extensive experimental
validation of MIN and MARAB compared to UCB and state-of-art risk-aware MAB
algorithms on artificial and real-world problems.Comment: 16 page
Functional Bandits
We introduce the functional bandit problem, where the objective is to find an
arm that optimises a known functional of the unknown arm-reward distributions.
These problems arise in many settings such as maximum entropy methods in
natural language processing, and risk-averse decision-making, but current
best-arm identification techniques fail in these domains. We propose a new
approach, that combines functional estimation and arm elimination, to tackle
this problem. This method achieves provably efficient performance guarantees.
In addition, we illustrate this method on a number of important functionals in
risk management and information theory, and refine our generic theoretical
results in those cases
Risk-averse multi-armed bandits and game theory
The multi-armed bandit (MAB) and game theory literature is mainly focused on the expected cumulative reward and the expected payoffs in a game, respectively. In contrast, the rewards and the payoffs are often random variables whose expected values only capture a vague idea of the overall distribution. The focus of this dissertation is to study the fundamental limits of the existing bandits and game theory problems in a risk-averse framework and propose new ideas that address the shortcomings. The author believes that human beings are mostly risk-averse, so studying multi-armed bandits and game theory from the point of view of risk aversion, rather than expected reward/payoff, better captures reality. In this manner, a specific class of multi-armed bandits, called explore-then-commit bandits, and stochastic games are studied in this dissertation, which are based on the notion of Risk-Averse Best Action Decision with Incomplete Information (R-ABADI, Abadi is the maiden name of the author's mother). The goal of the classical multi-armed bandits is to exploit the arm with the maximum score defined as the expected value of the arm reward. Instead, we propose a new definition of score that is derived from the joint distribution of all arm rewards and captures the reward of an arm relative to those of all other arms. We use a similar idea for games and propose a risk-averse R-ABADI equilibrium in game theory that is possibly different from the Nash equilibrium. The payoff distributions are taken into account to derive the risk-averse equilibrium, while the expected payoffs are used to find the Nash equilibrium. The fundamental properties of games, e.g. pure and mixed risk-averse R-ABADI equilibrium and strict dominance, are studied in the new framework and the results are expanded to finite-time games. Furthermore, the stochastic congestion games are studied from a risk-averse perspective and three classes of equilibria are proposed for such games. It is shown by examples that the risk-averse behavior of travelers in a stochastic congestion game can improve the price of anarchy in Pigou and Braess networks. Furthermore, the Braess paradox does not occur to the extent proposed originally when travelers are risk-averse.
We also study an online affinity scheduling problem with no prior knowledge of the task arrival rates and processing rates of different task types on different servers. We propose the Blind GB-PANDAS algorithm that utilizes an exploration-exploitation scheme to load balance incoming tasks on servers in an online fashion. We prove that Blind GB-PANDAS is throughput optimal, i.e. it stabilizes the system as long as the task arrival rates are inside the capacity region. The Blind GB-PANDAS algorithm is compared to FCFS, Max-Weight, and c-mu-rule algorithms in terms of average task completion time through simulations, where the same exploration-exploitation approach as Blind GB-PANDAS is used for Max-Weight and c--rule. The extensive simulations show that the Blind GB-PANDAS algorithm conspicuously outperforms the three other algorithms at high loads
Incentivizing the Dynamic Workforce: Learning Contracts in the Gig-Economy
In principal-agent models, a principal offers a contract to an agent to
perform a certain task. The agent exerts a level of effort that maximizes her
utility. The principal is oblivious to the agent's chosen level of effort, and
conditions her wage only on possible outcomes. In this work, we consider a
model in which the principal is unaware of the agent's utility and action
space. She sequentially offers contracts to identical agents, and observes the
resulting outcomes. We present an algorithm for learning the optimal contract
under mild assumptions. We bound the number of samples needed for the principal
obtain a contract that is within of her optimal net profit for every
Conditionally Risk-Averse Contextual Bandits
Contextual bandits with average-case statistical guarantees are inadequate in
risk-averse situations because they might trade off degraded worst-case
behaviour for better average performance. Designing a risk-averse contextual
bandit is challenging because exploration is necessary but risk-aversion is
sensitive to the entire distribution of rewards; nonetheless we exhibit the
first risk-averse contextual bandit algorithm with an online regret guarantee.
We conduct experiments from diverse scenarios where worst-case outcomes should
be avoided, from dynamic pricing, inventory management, and self-tuning
software; including a production exascale data processing system
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