A CPOMDP, or Constrained Partially Observable Markov Decision Process, gives two objectives for the system to optimize upon:

an reward function \(r(s,a)\) and a set of constraints \(c(s,a) \geq 0\). Specifically, we formulate it as a POMDP: \((S,A,\Omega), T, O ,R\), with an additional set of constraints \(\bold{C}\) and budgets \(\beta\).

Whereby, we seek to maximize the infinite-horizon reward \(\mathbb{E}_{t} \qty[R(a_{t}, s_{t})]\) subject to discounting, subject to:

\begin{equation} C_{i}(s,a) \leq \beta_{i}, \forall C_{i},\beta_{i} \in \bold{C}, \beta \end{equation}

crap to remember for AP Stats is a cram sheet for the AP Statistics exam.

95% confidence: \(z^*=1.96\)

• \(r=1\): perfect positive correlation
• \(r=-1\): perfect negative correlation
• \(r=0\): no correlation

• S: standard deviation of residuals
• R-sq: how much of varience in dep. var can be explained by indp. var

SE: estimate of standard deviation of the random var. that is slope.

Major Challenges

• data loss: crashes can happen, and not all data could be saved to disk
• inconsistency: crashes can happen in the middle of operations
  • crashes could occur when someone of the blocks that have been written to disk, but not others
  • inode and free lists don’t agree.

Ideally, filesystem operations should be atomic. Every operation should happen or not happen at all—but not halfway.

Case study: Block Cache Modification

Tradeoffs

The overall design tradeoffs between this: