Reaching a target in the plane with no information

Our main result is establishing the minimum cost (up to multiplicative constants) of reaching the target under both scenarios, and providing the optimal algorithm for the agent. For the static scenario the minimum cost is Θ((log⁡D+log⁡1r)D2/r), and for the dynamic scenario it is Θ((log⁡M+log⁡1r)M2/r), where M=max⁡(D,v). Under the latter scenario, the speed of the agent in our algorithm grows exponentially with time, and we prove that for an agent whose speed grows only polynomially with time, this cost is impossible to achieve.