For each of the following assertions, support your answer with examples or counterexamples:

For any local$-$search problem, hill$-$climbing will return a global optimum if the algorithm is run starting at

any state that is a neighbor of a neighbor of a globally optimal state.

In a nondeterministic, partially observable problem, improving an agent's transition model $($i$.$e$.,$

eliminating spurious outcomes that never actually occur$)$ will never increase the size of the agent's belief

states.

Stochastic hill climbing is guaranteed to arrive at a global optimum.

In a continuous space, gradient descent with a fixed step size is guaranteed to converge to a local or

global optimum.

Gradient descent finds the global optimum from any starting point if and only if the function is convex.

See rubric for grading.