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Dialogue Policy Optimisation Milica Gašić Dialogue Systems Group

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Reinforcement learning

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Dialogue as a partially observable Markov decision process (POMDP) atat stst s t+1 rtrt otot o t+1 State is unobservable State depends on a noisy observation Action selection (policy) is based on the distribution over all states at every time step t – belief state b(s t )

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Dialogue policy optimisation action state reward state

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Optimal Policy

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Reinforcement learning – the idea Take actions randomly Compute average reward Change policy to take actions that generated high reward

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Challenges in dialogue policy optimisation How to define the reward? Belief state is large and continuous Reinforcement learning takes many iterations

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Problem 1: The reward function Solution: Reward is a measure of how good the dialogue is

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Problem 2: Belief state is large and continuous Solution: Compress the belief state into a smaller scale summary space 1 J. Williams and S. Young (2005). "Scaling up POMDPs for Dialogue Management: The Summary POMDP Method." Original Belief Space Actions Policy Summary Space Summary Actions Summary Function Master Function Summary Policy

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Summary space Summary space contains features of the belief space that are important for learning This is hand-coded! It can contain probabilities of concepts, their values and so on! Continuous variables can be discretised into a grid

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Q-function Q-function measures the expected discounted reward that can be obtained at a grid point when an action is taken Takes into account the reward of the future actions Optimising the Q-function is equivalent to optimising the policy Discount Factor in (0,1] Reward Starting grid point Starting action Expectation with respect to policy π

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Online learning Reinforcement learning in direct interaction with the environment Actions are taken e-greedily Exploitation: choose action according to the best estimate of Q function Exploration: choose action randomly (with probability e)

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Monte Carlo control algorithm Initialise Q arbitrary Repeat Repeat for every turn in a dialogue Update belief state, map to summary space Record grid point, record reward Until the end of dialogue For each grid point sum up all rewards that followed Update Q function and policy

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How many iterations? Each grid point needs to be visited sufficiently enough to obtain good estimate If the grid is large then the estimate is not precise enough If there are lots of grid points then the policy optimization is slow In practice 10,000s dialogues are needed!

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Learning in interaction with a Simulated User Dialogue Manager Speech Generation Speech Understanding Dialogue State Dialogue Policy Expected Reward Optimise Policy

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Simulated user Various models Exhibit a variety of behaviour Imitate real users

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Agenda-based user simulator Consists of an agenda and a goal Goal: Concepts that describe the entity that the user wants Example: restaurant, cheap, Chinese Agenda Dialogue acts needed to elicit the user goal Dynamically changed during the dialogue Generated either deterministically or stochastically

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Learning with noisy input inform ( price = cheap, area = centre) inform ( price = cheap, area = south) 0.63 inform ( price = expensice ) 0.22 request ( area ) 0.15

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Evaluating a dialogue system Dialogue system consists of many components and joint evaluation is difficult What matters is the user experience Dialogue manager uses reward to optimise the dialogue policy This can also be used for evaluation

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Results

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Problem 3: Policy optimisation requires a lot of dialogues Policy optimisations requires 10,000s dialogues Solution: Take into account similarities between different belief states Essential ingredients Gaussian process Kernel function Outcome Fast policy optimisation

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The Q-function as a Gaussian Process The Q-function in a POMDP is the expected long-term reward from taking action a in belief state b(s). It can be modelled as a stochastic process – a Gaussian process to take into account the uncertainty of approximation

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VoiceMail example The user asks the system to save or delete the message. System actions: save, delete, confirm The user input is corrupted with noise, so the true dialogue state is unknown.

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Q-function as a Gaussian process belief state b(s)

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The role of kernel function in a Gaussian process The kernel function models correlation between different Q-function values Confirm Q-function value Action Belief state Confirm

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Exploration in online learning State space needs to be sufficiently explored to find the optimal path How to efficiently explore the space?

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Active learning in GP Reinforcement learning gives the uncertainty GP model for Q-function choose action that the model in uncertain about Exploration choose action with the highest expected reward Exploitation

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Results – Cambridge tourist information domain

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Learning in interaction with real people

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Conclusions Statistical dialogue modelling Automate dialogue manager optimisation Robust to speech recognition errors Enables fast learning Future work: Refined reward function

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