Machine learning system

1. A reinforcement learning system comprising:

an environment having multiple possible states;

an agent arranged to receive state information indicative of a current state of the environment and to generate an action signal dependent on the state information and a policy associated with the agent, the action signal being operable to cause a change in a state of the environment, the agent being further arranged to generate experience data dependent on the state information and information conveyed by the action signal;

a policy learner configured to process the experience data, whereby to update the policy associated with the agent;

a probabilistic model arranged to generate probabilistic data relating to future states of the environment; and

a model learner configured to process model input data to generate the probabilistic model,

wherein:

the environment comprises a domain having a temporal dimension;

the model input data comprises data indicative of events occurring in past states of the environment;

the agent is arranged to generate the action signal further in dependence on the probabilistic data;

the probabilistic model comprises a distribution of a stochastic intensity function, wherein an integral of the stochastic intensity function over a sub-region of the domain corresponds to a rate parameter of a Poisson distribution for a predicted number of events occurring in the sub-region; and

the model learner is configured to process the model input data to generate the probabilistic model by applying a Bayesian inference scheme to the model input data, the Bayesian inference scheme comprising:

generating a variational Gaussian process corresponding to a distribution of a latent function, the variational Gaussian process being dependent on a prior Gaussian process and a plurality of randomly-distributed inducing variables, the inducing variables having a variational distribution and expressible in terms of a plurality of Fourier components;

determining, using the data indicative of events occurring in past states of the environment, a set of parameters for the variational distribution, wherein determining the set of parameters comprises iteratively updating a set of intermediate parameters to determine an optimal value of an objective function, the objective function being dependent on the inducing variables and expressible in terms of the plurality of Fourier components; and

determining, from the variational Gaussian process and the determined set of parameters, the distribution of the stochastic intensity function, wherein the distribution of the stochastic intensity function corresponds to a distribution of a quadratic function of the latent function.

2. The system of claim 1 , wherein the model learner is further configured to process the experience data generated by the agent to update the probabilistic model.

3. The system of claim 1 , wherein each of the events occurring in a past state of the environment corresponds to an occurrence of an event in a physical system.

4. The system of claim 3 , wherein the agent is associated with an entity in the physical system.

5. The system of claim 4 , wherein the reinforcement learning system is operable to send a control signal, corresponding to the generated action signal, to the entity.

6. The system of claim 3 , wherein:

the physical system comprises one or more sensors; and

the agent is arranged to receive the state information from the one or more sensors.

7. The system of claim 4 , wherein:

each of the events occurring in a past state of the environment corresponds to a taxi request in a city; and

the agent is associated with a taxi in the city.