Optimistic linear programming gives logarithmic regret for irreducible MDPs

We present an algorithm called Optimistic Linear Programming (OLP) for learning to optimize average reward in an irreducible but otherwise unknown Markov decision process (MDP). OLP uses its experience so far to estimate the MDP. It chooses actions by optimistically maximizing estimated future rewards over a set of next-state transition probabilities that are close to the estimates, a computation that corresponds to solving linear programs. We show that the total expected reward obtained by OLP up to time T is within C(P) log T of the reward obtained by the optimal policy, where C(P) is an explicit, MDP-dependent constant. OLP is closely related to an algorithm proposed by Burnetas and Katehakis with four key differences: OLP is simpler, it does not require knowledge of the supports of transition probabilities, the proof of the regret bound is simpler, but our regret bound is a constant factor larger than the regret of their algorithm. OLP is also similar in flavor to an algorithm recently proposed by Auer and Ortner. But OLP is simpler and its regret bound has a better dependence on the size of the MDP.

REGAL : a regularization based algorithm for reinforcement learning in weakly communicating MDPs

We provide an algorithm that achieves the optimal regret rate in an unknown weakly communicating Markov Decision Process (MDP). The algorithm proceeds in episodes where, in each episode, it picks a policy using regularization based on the span of the optimal bias vector. For an MDP with S states and A actions whose optimal bias vector has span bounded by H, we show a regret bound of ~ O(HS p AT ). We also relate the span to various diameter-like quantities associated with the MDP, demonstrating how our results improve on previous regret bounds.

Parametrized actor-critic algorithms for finite-horizon MDPs

Due to their non-stationarity, finite-horizon Markov decision processes (FH-MDPs) have one probability transition matrix per stage. Thus the curse of dimensionality affects FH-MDPs more severely than infinite-horizon MDPs. We propose two parametrized 'actor-critic' algorithms to compute optimal policies for FH-MDPs. Both algorithms use the two-timescale stochastic approximation technique, thus simultaneously performing gradient search in the parametrized policy space (the 'actor') on a slower timescale and learning the policy gradient (the 'critic') via a faster recursion. This is in contrast to methods where critic recursions learn the cost-to-go proper. We show w.p 1 convergence to a set with the necessary condition for constrained optima. The proposed parameterization is for FHMDPs with compact action sets, although certain exceptions can be handled. Further, a third algorithm for stochastic control of stopping time processes is presented. We explain why current policy evaluation methods do not work as critic to the proposed actor recursion. Simulation results from flow-control in communication networks attest to the performance advantages of all three algorithms.

Solving MDPs using two-timescale simulated annealing with multiplicative weights

We develop extensions of the Simulated Annealing with Multiplicative Weights (SAMW) algorithm that proposed a method of solution of Finite-Horizon Markov Decision Processes (FH-MDPs). The extensions developed are in three directions: a) Use of the dynamic programming principle in the policy update step of SAMW b) A two-timescale actor-critic algorithm that uses simulated transitions alone, and c) Extending the algorithm to the infinite-horizon discounted-reward scenario. In particular, a) reduces the storage required from exponential to linear in the number of actions per stage-state pair. On the faster timescale, a 'critic' recursion performs policy evaluation while on the slower timescale an 'actor' recursion performs policy improvement using SAMW. We give a proof outlining convergence w.p. 1 and show experimental results on two settings: semiconductor fabrication and flow control in communication networks.

Solution of MDPS using simulation-based value iteration

This article proposes a three-timescale simulation based algorithm for solution of infinite horizon Markov Decision Processes (MDPs). We assume a finite state space and discounted cost criterion and adopt the value iteration approach. An approximation of the Dynamic Programming operator T is applied to the value function iterates. This 'approximate' operator is implemented using three timescales, the slowest of which updates the value function iterates. On the middle timescale we perform a gradient search over the feasible action set of each state using Simultaneous Perturbation Stochastic Approximation (SPSA) gradient estimates, thus finding the minimizing action in T. On the fastest timescale, the 'critic' estimates, over which the gradient search is performed, are obtained. A sketch of convergence explaining the dynamics of the algorithm using associated ODEs is also presented. Numerical experiments on rate based flow control on a bottleneck node using a continuous-time queueing model are performed using the proposed algorithm. The results obtained are verified against classical value iteration where the feasible set is suitably discretized. Over such a discretized setting, a variant of the algorithm of [12] is compared and the proposed algorithm is found to converge faster.

Anytime Algorithms for Solving Possibilistic MDPs and Hybrid MDPs

The ability of an agent to make quick, rational decisions in an uncertain environment is paramount for its applicability in realistic settings. Markov Decision Processes (MDP) provide such a framework, but can only model uncertainty that can be expressed as probabilities. Possibilistic counterparts of MDPs allow to model imprecise beliefs, yet they cannot accurately represent probabilistic sources of uncertainty and they lack the efficient online solvers found in the probabilistic MDP community. In this paper we advance the state of the art in three important ways. Firstly, we propose the first online planner for possibilistic MDP by adapting the Monte-Carlo Tree Search (MCTS) algorithm. A key component is the development of efficient search structures to sample possibility distributions based on the DPY transformation as introduced by Dubois, Prade, and Yager. Secondly, we introduce a hybrid MDP model that allows us to express both possibilistic and probabilistic uncertainty, where the hybrid model is a proper extension of both probabilistic and possibilistic MDPs. Thirdly, we demonstrate that MCTS algorithms can readily be applied to solve such hybrid models.

Efficient solutions to factored MDPs with imprecise transition probabilities

When modeling real-world decision-theoretic planning problems in the Markov Decision Process (MDP) framework, it is often impossible to obtain a completely accurate estimate of transition probabilities. For example, natural uncertainty arises in the transition specification due to elicitation of MOP transition models from an expert or estimation from data, or non-stationary transition distributions arising from insufficient state knowledge. In the interest of obtaining the most robust policy under transition uncertainty, the Markov Decision Process with Imprecise Transition Probabilities (MDP-IPs) has been introduced to model such scenarios. Unfortunately, while various solution algorithms exist for MDP-IPs, they often require external calls to optimization routines and thus can be extremely time-consuming in practice. To address this deficiency, we introduce the factored MDP-IP and propose efficient dynamic programming methods to exploit its structure. Noting that the key computational bottleneck in the solution of factored MDP-IPs is the need to repeatedly solve nonlinear constrained optimization problems, we show how to target approximation techniques to drastically reduce the computational overhead of the nonlinear solver while producing bounded, approximately optimal solutions. Our results show up to two orders of magnitude speedup in comparison to traditional ""flat"" dynamic programming approaches and up to an order of magnitude speedup over the extension of factored MDP approximate value iteration techniques to MDP-IPs while producing the lowest error of any approximation algorithm evaluated. (C) 2011 Elsevier B.V. All rights reserved.

The Melbourne Diabetes Prevention Study (MDPS) : study protocol for a randomized controlled trial

Background
Worldwide, type 2 diabetes (T2DM) prevalence has more than doubled over two decades. In Australia, diabetes is the second highest contributor to the burden of disease. Lifestyle modification programs comprising diet changes, weight loss and moderate physical activity, have been proven to reduce the incidence of T2DM in high risk individuals.

As part of the Council of Australia Governments, the State of Victoria committed to develop and support the diabetes prevention program ‘Life! Taking action on diabetes’ (Life!) which has direct lineage from effective clinical and implementation trials from Finland and Australia. The Melbourne Diabetes Prevention Study (MDPS) has been set up to evaluate the effectiveness and cost-effectiveness of a specific version of the Life! program.

Methods/design
We intend to recruit 796 participants for this open randomized clinical trial; 398 will be allocated to the intervention arm and 398 to the usual care arm. Several methods of recruitment will be used in order to maximize the number of participants. Individuals aged 50 to 75 years will be screened with a risk tool (AUSDRISK) to detect those at high risk of developing T2DM. Those with existing diabetes will be excluded. Intervention participants will undergo anthropometric and laboratory tests, and comprehensive surveys at baseline, following the fourth group session (approximately three months after the commencement of the intervention) and 12 months after commencement of the intervention, while control participants will undergo testing at baseline and 12 months only.

The intervention consists of an initial individual session followed by a series of five structured-group sessions. The first four group sessions will be carried out at two week intervals and the fifth session will occur eight months after the first group session. The intervention is based on the Health Action Process Approach (HAPA) model and sessions will empower and enable the participants to follow the five goals of the Life! program.

Discussion
This study will determine whether the effect of this intervention is larger than the effect of usual care in reducing central obesity and cardiovascular risk factors and thus the risk of developing diabetes and cardiovascular disease. Also it will evaluate how these two options compare economically.

The role of mitochondrial derived peptides (MDPs) in metabolism

The term "mitokines" refers to signals derived from mitochondria that have an impact on other cells or tissues (Durieux et al., 2011). Rather than being simply a set of DNA composed by 37 genes, the mitochondrial DNA (mtDNA) is quite complex and includes small RNAs (Mercer et al., 2011). Mitochondrial-derived peptides (MDPs) are encoded by functional short open reading frames (sORFs) in the mtDNA.

Energy Sharing for Multiple Sensor Nodes With Finite Buffers

We consider the problem of finding optimal energy sharing policies that maximize the network performance of a system comprising of multiple sensor nodes and a single energy harvesting (EH) source. Sensor nodes periodically sense the random field and generate data, which is stored in the corresponding data queues. The EH source harnesses energy from ambient energy sources and the generated energy is stored in an energy buffer. Sensor nodes receive energy for data transmission from the EH source. The EH source has to efficiently share the stored energy among the nodes to minimize the long-run average delay in data transmission. We formulate the problem of energy sharing between the nodes in the framework of average cost infinite-horizon Markov decision processes (MDPs). We develop efficient energy sharing algorithms, namely Q-learning algorithm with exploration mechanisms based on the epsilon-greedy method as well as upper confidence bound (UCB). We extend these algorithms by incorporating state and action space aggregation to tackle state-action space explosion in the MDP. We also develop a cross entropy based method that incorporates policy parameterization to find near optimal energy sharing policies. Through simulations, we show that our algorithms yield energy sharing policies that outperform the heuristic greedy method.

Learning Multirobot Hose Transportation and Deployment by Distributed Round-Robin Q-Learning

Multi-Agent Reinforcement Learning (MARL) algorithms face two main difficulties: the curse of dimensionality, and environment non-stationarity due to the independent learning processes carried out by the agents concurrently. In this paper we formalize and prove the convergence of a Distributed Round Robin Q-learning (D-RR-QL) algorithm for cooperative systems. The computational complexity of this algorithm increases linearly with the number of agents. Moreover, it eliminates environment non sta tionarity by carrying a round-robin scheduling of the action selection and execution. That this learning scheme allows the implementation of Modular State-Action Vetoes (MSAV) in cooperative multi-agent systems, which speeds up learning convergence in over-constrained systems by vetoing state-action pairs which lead to undesired termination states (UTS) in the relevant state-action subspace. Each agent's local state-action value function learning is an independent process, including the MSAV policies. Coordination of locally optimal policies to obtain the global optimal joint policy is achieved by a greedy selection procedure using message passing. We show that D-RR-QL improves over state-of-the-art approaches, such as Distributed Q-Learning, Team Q-Learning and Coordinated Reinforcement Learning in a paradigmatic Linked Multi-Component Robotic System (L-MCRS) control problem: the hose transportation task. L-MCRS are over-constrained systems with many UTS induced by the interaction of the passive linking element and the active mobile robots.

The Essential Dynamics Algorithm: Essential Results

This paper presents a novel algorithm for learning in a class of stochastic Markov decision processes (MDPs) with continuous state and action spaces that trades speed for accuracy. A transform of the stochastic MDP into a deterministic one is presented which captures the essence of the original dynamics, in a sense made precise. In this transformed MDP, the calculation of values is greatly simplified. The online algorithm estimates the model of the transformed MDP and simultaneously does policy search against it. Bounds on the error of this approximation are proven, and experimental results in a bicycle riding domain are presented. The algorithm learns near optimal policies in orders of magnitude fewer interactions with the stochastic MDP, using less domain knowledge. All code used in the experiments is available on the project's web site.

Multilinear and Integer Programming for Markov Decision Processes with Imprecise Probabilities

Markov Decision Processes (MDPs) are extensively used to encode sequences of decisions with probabilistic effects. Markov Decision Processes with Imprecise Probabilities (MDPIPs) encode sequences of decisions whose effects are modeled using sets of probability distributions. In this paper we examine the computation of Γ-maximin policies for MDPIPs using multilinear and integer programming. We discuss the application of our algorithms to “factored” models and to a recent proposal, Markov Decision Processes with Set-valued Transitions (MDPSTs), that unifies the fields of probabilistic and “nondeterministic” planning in artificial intelligence research. 

Ethical ramifications of corporatised legal practice

Ethical constraints applying to lawyers are largely found in formal restrictions in legislation - ethical duties arise as a result of a lawyer's service to the public - business ethics - corporatisation and the push for Multi-Disciplinary Practices (MDPs) - duty of confidentiality - avoiding conflicts of interest - the advent of MDP will add further pressures to lawyers juggling competing interests.