Prashant Solanki

Prashant Solanki, Isabelle El-Hajj, Jasper van Beers et al.

We unify Hamilton-Jacobi (HJ) reachability and Reinforcement Learning (RL) through a proposed running cost formulation. We prove that the resultant travel-cost value function is the unique bounded viscosity solution of a time-dependent Hamilton-Jacobi Bellman (HJB) Partial Differential Equation (PDE) with zero terminal data, whose negative sublevel set equals the strict backward-reachable tube. Using a forward reparameterization and a contraction inducing Bellman update, we show that fixed points of small-step RL value iteration converge to the viscosity solution of the forward discounted HJB. Experiments on a classical benchmark validate this connection by demonstrating convergence of learned value functions toward semi-Lagrangian HJB solutions and by quantifying approximation error across the state space. These results empirically support the theoretical analysis, showing that the proposed framework preserves reachability-based safety semantics while remaining compatible with deep RL implementations.

Prashant Solanki, Jasper Van Beers, Coen De Visser

This paper studies obstacle avoidance under translation invariant dynamics using an avoid-side travel cost Hamilton Jacobi formulation. For running costs that are zero outside an obstacle and strictly negative inside it, we prove that the value function is non-positive everywhere, equals zero exactly outside the avoid set, and is strictly negative exactly on it. Under translation invariance, this yields a reuse principle: the value of any translated obstacle is obtained by translating a single template value function. We show that the pointwise minimum of translated template values exactly characterizes the union of the translated single-obstacle avoid sets and provides a conservative inner certificate of unavoidable collision in clutter. To reduce conservatism, we introduce a blockwise composition framework in which subsets of obstacles are merged and solved jointly. This yields a hierarchy of conservative certificates from singleton reuse to the exact clutter value, together with monotonicity under block merging and an exactness criterion based on the existence of a common clutter avoiding control. The framework is illustrated on a Dubins car example in a repeated clutter field.

Prashant Solanki, Nikolaus Vertovec, Yannik Schnitzer et al.

Recent approaches to leveraging deep learning for computing reachable sets of continuous-time dynamical systems have gained popularity over traditional level-set methods, as they overcome the curse of dimensionality. However, as with level-set methods, considerable care needs to be taken in limiting approximation errors, particularly since no guarantees are provided during training on the accuracy of the learned reachable set. To address this limitation, we introduce an epsilon-approximate Hamilton-Jacobi Partial Differential Equation (HJ-PDE), which establishes a relationship between training loss and accuracy of the true reachable set. To formally certify this approximation, we leverage Satisfiability Modulo Theories (SMT) solvers to bound the residual error of the HJ-based loss function across the domain of interest. Leveraging Counter Example Guided Inductive Synthesis (CEGIS), we close the loop around learning and verification, by fine-tuning the neural network on counterexamples found by the SMT solver, thus improving the accuracy of the learned reachable set. To the best of our knowledge, Certified Approximate Reachability (CARe) is the first approach to provide soundness guarantees on learned reachable sets of continuous dynamical systems.

Prashant Solanki, Kwan Hui Lim, Aaron Harwood

With the prevalence of online social networking sites (OSNs) and mobile devices, people are increasingly reliant on a variety of OSNs for keeping in touch with family and friends, and using it as a source of information. For example, a user might utilise multiple OSNs for different purposes, such as using Flickr to share holiday pictures with family and friends, and Twitter to post short messages about their thoughts. Identifying the same user across multiple OSNs is an important task as this allows us to understand the usage patterns of users among different OSNs, make recommendations when a user registers for a new OSN, and various other useful applications. To address this problem, we proposed an algorithm based on the multilayer perceptron using various types of features, namely: (i) user profile, such as name, location, description; (ii) temporal distribution of user generated content; and (iii) embedding based on user name, real name and description. Using a Twitter and Flickr dataset of users and their posting activities, we perform an empirical study on how these features affect the performance of user identification across the two OSNs and discuss our main findings based on the different features.