Abstract: A system configured to determine candidate sets of values for enforceable parameters for a physical system, and for each candidate set of values, determine a performance measurement for the physical system and generate a data point having an input portion indicative of the candidate set of values and an output portion indicative of the determined performance measurement. The system is further arranged to augment each data point to include an additional dimension comprising a bias value; project each augmented data point onto a surface of a unit hypersphere of the first number of dimensions; determine, using the projected augmented data points, a set of parameter values for a sparse variational Gaussian process, GP, on said unit hypersphere; and determine, using the sparse variational GP with the determined set of parameter values, a further set of values for the set of enforceable parameters.

Abstract: A computer-implemented method of processing data comprising a plurality of observations associated with respective ordered input values to train a Gaussian process (GP) to model the data. The method includes initialising an ordered plurality of inducing input locations, and initialising parameters of a multivariate Gaussian distribution over a set of inducing states, each inducing state having components corresponding to a Markovian GP and one or more derivatives of the Markovian GP at a respective one of the inducing inputs. The initialised parameters include a mean vector and a banded Cholesky factor of a precision matrix for the multivariate Gaussian distribution. The method further includes iteratively modifying the parameters of the multivariate Gaussian distribution, to increase or decrease an objective function corresponding to a variational lower bound of a marginal log-likelihood of the observations under the Markovian GP.

Abstract: First parameters of a variational Gaussian process (VGP) (including a positive-definite matrix-valued slack parameter) are initialized and iteratively modified change an objective function comprising an expected log-likelihood for each training data item under a respective Gaussian distribution with a predictive variance depending on the slack parameter. Modifying the first parameters comprises, for each training data item, determining a respective gradient estimator for the expected log-likelihood and modifying the first parameters in dependence on the determined gradient estimators. At an optimal value of the slack parameter, the slack parameter equals an inverse of a covariance matrix for the set of inducing variables, and the objective function corresponds to a variational lower bound of a marginal log-likelihood for a posterior distribution corresponding to the GP prior conditioned on the training data.

Abstract: A computer-implemented method of processing training data comprising a plurality of training data items to determine parameters of a Gaussian process (GP) model comprising a variational Gaussian process (VGP) corresponding to a GP prior conditioned and marginalized with respect to a set of randomly-distributed inducing variables includes initializing first parameters of the VGP including a positive-definite matrix-valued slack parameter, and iteratively modifying the first parameters to increase or decrease an objective function comprising an expected log-likelihood for each training data item under a respective Gaussian distribution with a predictive variance depending on the slack parameter. At each iteration, modifying the first parameters comprises, for each training data item, determining a respective gradient estimator for the expected log-likelihood using a respective one of a plurality of processor cores, and modifying the first parameters in dependence on the determined gradient estimators.

Abstract: A system configured to determine candidate sets of values for enforceable parameters for a physical system, and for each candidate set of values, determine a performance measurement for the physical system and generate a data point having an input portion indicative of the candidate set of values and an output portion indicative of the determined performance measurement. The system is further arranged to augment each data point to include an additional dimension comprising a bias value; project each augmented data point onto a surface of a unit hypersphere of the first number of dimensions; determine, using the projected augmented data points, a set of parameter values for a sparse variational Gaussian process, GP, on said unit hypersphere; and determine, using the sparse variational GP with the determined set of parameter values, a further set of values for the set of enforceable parameters.

Abstract: A system configured to determine candidate sets of values for enforceable parameters for a physical system, and for each candidate set of values, determine a performance measurement for the physical system and generate a data point having an input portion indicative of the candidate set of values and an output portion indicative of the determined performance measurement. The system is further arranged to augment each data point to include an additional dimension comprising a bias value; project each augmented data point onto a surface of a unit hypersphere of the first number of dimensions; determine, using the projected augmented data points, a set of parameter values for a sparse variational Gaussian process, GP, on said unit hypersphere; and determine, using the sparse variational GP with the determined set of parameter values, a further set of values for the set of enforceable parameters.

Abstract: A reinforcement learning system comprises an environment (having multiple possible states), and agent, and a policy learner.. The agent is arranged to receive state information indicative of a current environment state and generate an action signal dependent on the state information and a policy associated with the agent, where the action signal is operable to cause an environment-state change. The agent is further arranged to generate experience data dependent on the state information and information conveyed by the action signal. The policy learner is configured to process the experience data in order to update the policy associated with the agent. The reinforcement learning system further comprises a probabilistic model arranged to generate, dependent on the current state of the environment, probabilistic data relating to future states of the environment, and the agent is further arranged to generate the action signal in dependence on the probabilistic data.

Abstract: A data processing system includes first memory circuitry arranged to store a dataset and second memory circuitry arranged to store a set of parameters of a statistical model. The system includes a sampler for transferring a sampled mini-batch of observation points from the first memory circuitry to the second memory circuitry, and an inference module arranged to determine, for each sampled observation point, an estimator for a component of a gradient component of an objective function. The system includes a recognition network module arranged to: process the sampled observation points using a recognition network to generate, for each sampled observation point, a respective set of control coefficients; and modify, for each sampled observation point, the respective estimator using the respective set of control coefficients. The inference module is arranged to update the parameters of the statistical model in accordance with a gradient estimate based on the modified stochastic estimators.

Abstract: There is described a machine learning system comprising a first subsystem and a second subsystem remote from the first subsystem. The first subsystem comprises an environment having multiple possible states and a decision making subsystem comprising one or more agents. Each agent is arranged to receive state information indicative of a current state of the environment and to generate an action signal dependent on the received state information and a policy associated with that agent, the action signal being operable to cause a change in a state of the environment. Each agent is further arranged to generate experience data dependent on the received state information and information conveyed by the action signal. The first subsystem includes a first network interface configured to send said experience data to the second subsystem and to receive policy data from the second subsystem.

Abstract: A method includes: receiving training data comprising a plurality of training data items, each training data item labelled under a respective class and comprising a elements arranged in conformity with a structured representation having an associated coordinate system; determining patches of the training data, each patch comprising a subset of the elements of a respective training data item and being associated with a location within the co-ordinate system of the structured representation; and initialising a set of parameters for a Gaussian process. The method further includes iteratively: processing pairs of the determined patches, using a patch response kernel to determine patch response data; determining, using the patch response data, entries of a covariance matrix; and updating the set of parameters in dependence on the determined entries of the covariance matrix.

Abstract: A reinforcement learning system comprises an environment (having multiple possible states), and agent, and a policy learner.. The agent is arranged to receive state information indicative of a current environment state and generate an action signal dependent on the state information and a policy associated with the agent, where the action signal is operable to cause an environment-state change. The agent is further arranged to generate experience data dependent on the state information and information conveyed by the action signal. The policy learner is configured to process the experience data in order to update the policy associated with the agent. The reinforcement learning system further comprises a probabilistic model arranged to generate, dependent on the current state of the environment, probabilistic data relating to future states of the environment, and the agent is further arranged to generate the action signal in dependence on the probabilistic data.

Abstract: A method includes: receiving training data comprising a plurality of training data items, each training data item labelled under a respective class and comprising a elements arranged in conformity with a structured representation having an associated coordinate system; determining patches of the training data, each patch comprising a subset of the elements of a respective training data item and being associated with a location within the co-ordinate system of the structured representation; and initialising a set of parameters for a Gaussian process. The method further includes iteratively: processing pairs of the determined patches, using a patch response kernel to determine patch response data; determining, using the patch response data, entries of a covariance matrix; and updating the set of parameters in dependence on the determined entries of the covariance matrix.