POMDPs to solve Active Sensing Problem: where gathering information is the explicit goal and not a means to do something. Meaning, we can’t train them using state-only reward functions (i.e. reward is based on belief and not state).

Directly reward the reduction of uncertainty: belief-based reward framework which you can just tack onto the existing solvers.

To do this, we want to define some reward directly over the belief space which assigns rewards based on uncertainty reduction:

For some predicate \(P\):

\begin{equation} P: \qty {TM} \to \qty {0,1} \end{equation}

think of \(0\) (false), \(1\) (true), where \(P\) satisfies:

1. non trivial: there are Turing Machines \(M_{yes}\), \(M_{no}\) such that \(P(M_{yes}) = 1\), and \(P(M_{no}) = 0\)
2. semantic: for all Turing Machines \(M_1\) and \(M_2\), if \(L(M_1) = L(M_2)\) then \(P(M_1) = P(M_2)\)

then, the language \(L = \qty {M \mid P(M) = 1}\) is undecidable.

to do this, check if \(P(M_{\emptyset}) = 0\) or \(P(M_{\emptyset}) = 1\); if the former, then ATM reduces to your language and your language isn’t decidable. If the latter, than not ATM reduces to your language and your language isn’t recognizable.

Richard Nixon is an American president, but pretty much is the watergate guy.

• Served in House and Senate
• Eisenhower’s VP for 8 years
• Lost first to JFK

Richard Nixon is a pragmatist; he pushes economy out of presession via Keynsian Politics.

Richard Nixon also realized that the large southern population can be motivated via racist policies, so he shifted the .

political positions of Richard Nixon

• Richard Nixon’s Treatment against the Vietnam War
• Richard Nixon’s Foreign Policy

Richard Nixon’s foreign policy is marked by the “Nixon Doctrine”: shifting the burden of military containment to allies.

• Supports China as a means against USSR
• Negotiate with the USSR to lower tension
• Shifts focus into building and supporting allies

Richard Nixon proposed the strategy of vietnamization as a treatment to the Vietnam War. He also expanded to Cambodia. To beat the Viet Cong into submission, he initialized the Operation Linebacker campaign.