You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
We present a method for Temporal Difference (TD) learning that addresses several challenges faced by robots learning to navigate in a marine environment. For improved data efficiency, our method reduces TD updates to Gaussian Process regression. To make predictions amenable to online settings, we introduce a sparse approximation with improved quality over current rejection-based sparse methods. We derive the predictive value function posterior and use the moments to obtain a new algorithm for model-free policy evaluation, SPGP-SARSA. With simple changes, we show SPGP-SARSA can be reduced to a model-based equivalent, SPGP-TD. We perform comprehensive simulation studies and also conduct physical learning trials with an underwater robot. Our results show SPGP-SARSA can outperform the state-of-the-art sparse method, replicate the prediction quality of its exact counterpart, and be applied to solve underwater navigation tasks.

Cited Abstract(s):
[1]: Gaussian Process Temporal Difference (GPTD) learning offers a Bayesian solution to the policy evaluation problem of reinforcement learning. In this paper we extend the GPTD framework by addressing two pressing issues, which were not adequately treated in the original GPTD paper (, 2003). The first is the issue of stochasticity in the state transitions, and the second is concerned with action selection and policy improvement. We present a new generative model for the value function, deduced from its relation with the discounted return. We derive a corresponding on-line algorithm for learning the posterior moments of the value Gaussian process. We also present a SARSA based extension of GPTD, termed GPSARSA, that allows the selection of actions and the gradual improvement of policies without requiring a world-model.
When it comes to other approximate methods, the state-of-the-art uses a low-rank approximation to the full covariance matrix [1] : @math , where @math is a projection matrix. Before adding new data to the active set, checks if new data points increase the conditional covariance by a desired error threshold, @math . In Section , we compare the approximation quality of and .