Browsing by Author "Akbarzadeh, Nima"

Now showing 1 - 3 of 3
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    Gambler's ruin bandit problem
    (IEEE, 2017) Akbarzadeh, Nima; Tekin, Cem
    In this paper, we propose a new multi-armed bandit problem called the Gambler's Ruin Bandit Problem (GRBP). In the GRBP, the learner proceeds in a sequence of rounds, where each round is a Markov Decision Process (MDP) with two actions (arms): a continuation action that moves the learner randomly over the state space around the current state; and a terminal action that moves the learner directly into one of the two terminal states (goal and dead-end state). The current round ends when a terminal state is reached, and the learner incurs a positive reward only when the goal state is reached. The objective of the learner is to maximize its long-term reward (expected number of times the goal state is reached), without having any prior knowledge on the state transition probabilities. We first prove a result on the form of the optimal policy for the GRBP. Then, we define the regret of the learner with respect to an omnipotent oracle, which acts optimally in each round, and prove that it increases logarithmically over rounds. We also identify a condition under which the learner's regret is bounded. A potential application of the GRBP is optimal medical treatment assignment, in which the continuation action corresponds to a conservative treatment and the terminal action corresponds to a risky treatment such as surgery.
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    Online learning in limit order book trade execution
    (IEEE, 2018) Akbarzadeh, Nima; Tekin, Cem; Schaar, M. V.
    In this paper, we propose an online learning algorithm for optimal execution in the limit order book of a financial asset. Given a certain amount of shares to sell and an allocated time window to complete the transaction, the proposed algorithm dynamically learns the optimal number of shares to sell via market orders at pre-specified time-slots within the allocated time interval. We model this problem as a Markov Decision Process (MDP), which is then solved by dynamic programming. First, we prove that the optimal policy has a specific form, which requires either selling no shares or the maximum allowed amount of shares at each time slot. Then, we consider the learning problem, where the state transition probabilities are unknown and need to be learned on-the-fly. We propose a learning algorithm that exploits the form of the optimal policy when choosing the amount to trade. Our numerical results show that the proposed algorithm performs significantly better than the traditional Q-learning algorithm by exploiting the structure of the problem.
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    Online learning in structured Markov decision processes
    (2017-07) Akbarzadeh, Nima
    This thesis proposes three new multi-armed bandit problems, in which the learner proceeds in a sequence of rounds where each round is a Markov Decision Process (MDP). The learner's goal is to maximize its cumulative reward without any a priori knowledge on the state transition probabilities. The rst problem considers an MDP with sorted states and a continuation action that moves the learner to an adjacent state; and a terminal action that moves the learner to a terminal state (goal or dead-end state). In this problem, a round ends and the next round starts when a terminal state is reached, and the aim of the learner in each round is to reach the goal state. First, the structure of the optimal policy is derived. Then, the regret of the learner with respect to an oracle, who takes optimal actions in each round is de ned, and a learning algorithm that exploits the structure of the optimal policy is proposed. Finally, it is shown that the regret either increases logarithmically over rounds or becomes bounded. In the second problem, we investigate the personalization of a clinical treatment. This process is modeled as a goal-oriented MDP with dead-end states. Moreover, the state transition probabilities of the MDP depends on the context of the patients. An algorithm that uses the rule of optimism in face of uncertainty is proposed to maximize the number of rounds in which the goal state is reached. In the third problem, we propose an online learning algorithm for optimal execution in the limit order book of a nancial asset. Given a certain amount of shares to sell and an allocated time to complete the transaction, the proposed algorithm dynamically learns the optimal number of shares to sell at each time slot of the allocated time. We model this problem as an MDP, and derive the form of the optimal policy.