Batched bandit problems

Motivated by practical applications, chiefly clinical trials, we study the regret achievable for stochastic bandits under the constraint that the employed policy must split trials into a small number of batches. We propose a simple policy, and show that a very small number of batches gives close to minimax optimal regret bounds. As a byproduct, we derive optimal policies with low switching cost for stochastic bandits.Comment: Published at http://dx.doi.org/10.1214/15-AOS1381 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

An Analytical Solution for Probabilistic Guarantees of Reservation Based Soft Real-Time Systems

We show a methodology for the computation of the probability of deadline miss for a periodic real-time task scheduled by a resource reservation algorithm. We propose a modelling technique for the system that reduces the computation of such a probability to that of the steady state probability of an infinite state Discrete Time Markov Chain with a periodic structure. This structure is exploited to develop an efficient numeric solution where different accuracy/computation time trade-offs can be obtained by operating on the granularity of the model. More importantly we offer a closed form conservative bound for the probability of a deadline miss. Our experiments reveal that the bound remains reasonably close to the experimental probability in one real-time application of practical interest. When this bound is used for the optimisation of the overall Quality of Service for a set of tasks sharing the CPU, it produces a good sub-optimal solution in a small amount of time.Comment: IEEE Transactions on Parallel and Distributed Systems, Volume:27, Issue: 3, March 201

Statistical Model Checking for Stochastic Hybrid Systems

This paper presents novel extensions and applications of the UPPAAL-SMC model checker. The extensions allow for statistical model checking of stochastic hybrid systems. We show how our race-based stochastic semantics extends to networks of hybrid systems, and indicate the integration technique applied for implementing this semantics in the UPPAAL-SMC simulation engine. We report on two applications of the resulting tool-set coming from systems biology and energy aware buildings.Comment: In Proceedings HSB 2012, arXiv:1208.315

Reasoning About the Reliability of Multi-version, Diverse Real-Time Systems

This paper is concerned with the development of reliable real-time systems for use in high integrity applications. It advocates the use of diverse replicated channels, but does not require the dependencies between the channels to be evaluated. Rather it develops and extends the approach of Little wood and Rush by (for general systems) by investigating a two channel system in which one channel, A, is produced to a high level of reliability (i.e. has a very low failure rate), while the other, B, employs various forms of static analysis to sustain an argument that it is perfect (i.e. it will never miss a deadline). The first channel is fully functional, the second contains a more restricted computational model and contains only the critical computations. Potential dependencies between the channels (and their verification) are evaluated in terms of aleatory and epistemic uncertainty. At the aleatory level the events ''A fails" and ''B is imperfect" are independent. Moreover, unlike the general case, independence at the epistemic level is also proposed for common forms of implementation and analysis for real-time systems and their temporal requirements (deadlines). As a result, a systematic approach is advocated that can be applied in a real engineering context to produce highly reliable real-time systems, and to support numerical claims about the level of reliability achieved