We consider a restless multi-armed bandit in which each arm can be in one of two states. When an arm is sampled, the state of the arm is not available to the sampler. Instead, a binary signal with a known randomness that depends on the state of the arm is available. No signal is available if the arm is not sampled. An arm-dependent reward is accrued from each sampling. In each time step, each arm changes state according to known transition probabilities which in turn depend on whether the arm is sampled or not sampled. Since the state of the arm is never visible and has to be inferred from the current belief and a possible binary signal, we call this the hidden Markov bandit. Our interest is in a policy to select the arm(s) in each time step that maximizes the infinite horizon discounted reward. Specifically, we seek the use of Whittle's index in selecting the arms.We first analyze the single-armed bandit and show that in general, it admits an approximate threshold-type optimal policy when there is a positive reward for the 'no-sample' action. We also identify several special cases for which the threshold policy is indeed the optimal policy. Next, we show that such a singlearmed bandit also satisfies an approximate-indexability property. For the case when the single-armed bandit admits a thresholdtype optimal policy, we perform the calculation of the Whittle index for each arm. Numerical examples illustrate the analytical results.

Analog and digital circuit designs have been proposed to mimic the biological neuron in CMOS compatible learning circuits for "brain" like computing. However, the adaptation of such conventional circuit based strategies requires many devices, large areas and hence power consumption. We propose a neuronal device based on the well-investigated impact-ionization based NPN selector on an SOI platform. The neuronal device has a small footprint (225*F 2 ) and low active power (11.5nW/spike) and provides ~10,000x speed-up over biological timescales. In comparison to analog neuron, ultra-high density (>60x improvement) and low power operation (>5x improvement) are demonstrated.

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