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 input data comprising a plurality of samples arranged on a regular grid within a finite sampling window, to train parameters for a kernel of a Gaussian process for modelling the data. The parameters are associated with a mixture of spectral components representing a spectral density of the kernel. The method includes: initialising the parameters; determining a cut-off frequency for delimiting a low-frequency range and a high-frequency range, the cut-off frequency being an integer multiple of a fundamental frequency corresponding to a reciprocal size of the sampling window; performing a discrete Fourier transform on the input data to determine frequency domain data; and processing a portion of the frequency domain data within the low-frequency range to determine smoothed input data.

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 machine learning system comprises: a set of agents, each having associated processing circuitry and associated memory circuitry, the associated memory circuitry of each agent holding a respective policy for selecting an action in dependence on the agent making an observation of an environment; and a meta-agent having associated processing circuitry and associated memory circuitry. The associated memory circuitry of each agent further holds program code which, when executed by the associated processing circuitry of that agent, causes that agent to update iteratively the respective policy of that agent, each iteration of the updating comprising, for each of a sequence of time steps: making an observation of the environment; selecting and performing an action depending on the observation and the respective policy; and determining a reward in response to performing the selected action, the reward depending on a reward modifier parameter.

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.