This thesis focuses on the problem of scalable optimization of dialogue behaviour in speech-based conversational systems using reinforcement learning. Most previous investigations in dialogue strategy learning have proposed flat reinforcement learning methods, which are more suitable for small-scale spoken dialogue systems. This research formulates the problem in terms of Semi-Markov Decision Processes (SMDPs), and proposes two hierarchical reinforcement learning methods to optimize sub-dialogues rather than full dialogues. The first method uses a hierarchy of SMDPs, where every SMDP ignores irrelevant state variables and actions in order to optimize a sub-dialogue. The second method extends the first one by constraining every SMDP in the hierarchy with prior expert knowledge. The latter method proposes a learning algorithm called 'HAM+HSMQ-Learning', which combines two existing algorithms in the literature of hierarchical reinforcement learning. Whilst the first method generates fully-learnt behaviour, the second one generates semi-learnt behaviour. In addition, this research proposes a heuristic dialogue simulation environment for automatic dialogue strategy learning. Experiments were performed on simulated and real environments based on a travel planning spoken dialogue system. Experimental results provided evidence to support the following claims: First, both methods scale well at the cost of near-optimal solutions, resulting in slightly longer dialogues than the optimal solutions. Second, dialogue strategies learnt with coherent user behaviour and conservative recognition error rates can outperform a reasonable hand-coded strategy. Third, semi-learnt dialogue behaviours are a better alternative (because of their higher overall performance) than hand-coded or fully-learnt dialogue behaviours. Last, hierarchical reinforcement learning dialogue agents are feasible and promising for the (semi) automatic design of adaptive behaviours in larger-scale spoken dialogue systems. This research makes the following contributions to spoken dialogue systems which learn their dialogue behaviour. First, the Semi-Markov Decision Process (SMDP) model was proposed to learn spoken dialogue strategies in a scalable way. Second, the concept of 'partially specified dialogue strategies' was proposed for integrating simultaneously hand-coded and learnt spoken dialogue behaviours into a single learning framework. Third, an evaluation with real users of hierarchical reinforcement learning dialogue agents was essential to validate their effectiveness in a realistic environment.

Classical value estimation reinforcement learning algorithms do not perform very well in dynamic environments. On the other hand, the reinforcement learning of animals is quite flexible: they can adapt to dynamic environments very quickly and deal with noisy inputs very effectively. One feature that may contribute to animals' good performance in dynamic environments is that they learn and perceive the time to reward. In this research, we attempt to learn and perceive the time to reward and explore situations where the learned time information can be used to improve the performance of the learning agent in dynamic environments. The type of dynamic environments that we are interested in is that type of switching environment which stays the same for a long time, then changes abruptly, and then holds for a long time before another change. The type of dynamics that we mainly focus on is the time to reward, though we also extend the ideas to learning and perceiving other criteria of optimality, e.g. the discounted return, so that they can still work even when the amount of reward may also change. Specifically, both the mean and variance of the time to reward are learned and then used to detect changes in the environment and to decide whether the agent should give up a suboptimal action. When a change in the environment is detected, the learning agent responds specifically to the change in order to recover quickly from it. When it is found that the current action is still worse than the optimal one, the agent gives up this time's exploration of the action and then remakes its decision in order to avoid longer than necessary exploration. The results of our experiments using two real-world problems show that they have effectively sped up learning, reduced the time taken to recover from environmental changes, and improved the performance of the agent after the learning converges in most of the test cases compared with classical value estimation reinforcement learning algorithms. In addition, we have successfully used spiking neurons to implement various phenomena of classical conditioning, the simplest form of animal reinforcement learning in dynamic environments, and also pointed out a possible implementation of instrumental conditioning and general reinforcement learning using similar models.

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In this thesis we investigate single and multi-player stochastic dynamic optimization prob-lems. We consider both discrete and continuous time processes. In the multi-player setup we investigate zero-sum games with both complete and partial information. We study partially observable stochastic games with average cost criterion and the state process be-ing discrete time controlled Markov chain. The idea involved in studying this problem is to replace the original unobservable state variable with a suitable completely observable state variable. We establish the existence of the value of the game and also obtain optimal strategies for both players. We also study a continuous time zero-sum stochastic game with complete observation. In this case the state is a pure jump Markov process. We investigate the nite horizon total cost criterion. We characterise the value function via appropriate Isaacs equations. This also yields optimal Markov strategies for both players. In the single player setup we investigate risk-sensitive control of continuous time Markov chains. We consider both nite and in nite horizon problems. For the nite horizon total cost problem and the in nite horizon discounted cost problem we characterise the value function as the unique solution of appropriate Hamilton Jacobi Bellman equations. We also derive optimal Markov controls in both the cases. For the in nite horizon average cost case we shown the existence of an optimal stationary control. we also give a value iteration scheme for computing the optimal control in the case of nite state and action spaces. Further we introduce a new class of stochastic processes which we call stochastic processes with \age-dependent transition rates". We give a rigorous construction of the process. We prove that under certain assunptions the process is Feller. We also compute the limiting probabilities for our process. We then study the controlled version of the above process. In this case we take the risk-neutral cost criterion. We solve the in nite horizon discounted cost problem and the average cost problem for this process. The crucial step in analysing these problems is to prove that the original control problem is equivalent to an appropriate semi-Markov decision problem. Then the value functions and optimal controls are characterised using this equivalence and the theory of semi-Markov decision processes (SMDP). The analysis of nite horizon problems becomes di erent from that of in nite horizon problems because of the fact that in this case the idea of converting into an equivalent SMDP does not seem to work. So we deal with the nite horizon total cost problem by showing that our problem is equivalent to another appropriately de ned discrete time Markov decision problem. This allows us to characterise the value function and to nd an optimal Markov control.

Two different sets of problems are addressed in this thesis. The first one is on partially observed semi-Markov Games (POSMG) and the second one is on semi-Markov modulated financial market model. In this thesis we study a partially observable semi-Markov game in the infinite time horizon. The study of a partially observable game (POG) involves three major steps: (i) construct an equivalent completely observable game (COG), (ii) establish the equivalence between POG and COG by showing that if COG admits an equilibrium, POG does so, (iii) study the equilibrium of COG and find the corresponding equilibrium of original partially observable problem. In case of infinite time horizon game problem there are two different payoff criteria. These are discounted payoff criterion and average payoff criterion. At first a partially observable semi-Markov decision process on general state space with discounted cost criterion is studied. An optimal policy is shown to exist by considering a Shapley’s equation for the corresponding completely observable model. Next the discounted payoff problem is studied for two-person zero-sum case. A saddle point equilibrium is shown to exist for this case. Then the variable sum game is investigated. For this case the Nash equilibrium strategy is obtained in Markov class under suitable assumption. Next the POSMG problem on countable state space is addressed for average payoff criterion. It is well known that under this criterion the game problem do not have a solution in general. To ensure a solution one needs some kind of ergodicity of the transition kernel. We find an appropriate ergodicity of partially observed model which in turn induces a geometric ergodicity to the equivalent model. Using this we establish a solution of the corresponding average payoff optimality equation (APOE). Thus the value and a saddle point equilibrium is obtained for the original partially observable model. A value iteration scheme is also developed to find out the average value of the game. Next we study the financial market model whose key parameters are modulated by semi-Markov processes. Two different problems are addressed under this market assumption. In the first one we show that this market is incomplete. In such an incomplete market we find the locally risk minimizing prices of exotic options in the Follmer Schweizer framework. In this model the stock prices are no more Markov. Generally stock price process is modeled as Markov process because otherwise one may not get a pde representation of price of a contingent claim. To overcome this difficulty we find an appropriate Markov process which includes the stock price as a component and then find its infinitesimal generator. Using Feynman-Kac formula we obtain a system of non-local partial differential equations satisfied by the option price functions in the mildsense. .Next this system is shown to have a classical solution for given initial or boundary conditions. Then this solution is used to have a F¨ollmer Schweizer decomposition of option price. Thus we obtain the locally risk minimizing prices of different options. Furthermore we obtain an integral equation satisfied by the unique solution of this system. This enable us to compute the price of a contingent claim and find the risk minimizing hedging strategy numerically. Further we develop an efficient and stable numerical method to compute the prices. Beside this work on derivative pricing, the portfolio optimization problem in semi-Markov modulated market is also studied in the thesis. We find the optimal portfolio selections by optimizing expected utility of terminal wealth. We also obtain the optimal portfolio selections under risk sensitive criterion for both finite and infinite time horizon.