Gambler's Ruin Bandit Problem

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

Inverse Prism based on Temporal Discontinuity and Spatial Dispersion

We introduce the concept of the inverse prism as the dual of the conventional prism and deduce from this duality an implementation of it based on temporal discontinuity and spatial dispersion provided by anisotropy. Moreover, we show that this inverse prism exhibits the following three unique properties: chromatic refraction birefringence, ordinary-monochromatic and extraordinary- polychromatic temporal refraction, and linear-to-Lissajous polarization transformation

Flexible-Resolution, Arbitrary-Input and Tunable Rotman Lens Spectrum Decomposer (RL-SD)

We present an enhanced design -- in terms of resolution flexibility, input port position arbitrariness and frequency-range tunability -- of the planar Rotman lens spectrum decomposer (RL-SD). This enhancement is achieved by manipulating the output port locations through proper sampling of the frequency-position law of the RL-SD, inserting a calibration array compensating for frequency deviation induced by input modification and introducing port switching, respectively. A complete design procedure is provided and two enhanced RL-SD prototypes, with uniform port distribution and uniform frequency resolution, respectively, are numerically and experimentally demonstrated