optimise.sequential.eu {bdpopt} R Documentation

## Optimise Sequential Expected Utility

### Description

Optimise the expected utility for a sequential decision problem. The optimisation proceeds by backward induction, computing the optimal decision and corresponding expected utility at each stage over a grid for the current state summarising the posterior distribution of the unknown parameter.

### Usage

```optimise.sequential.eu(dp, mins, maxs, steps, n.sims, state.start = NA)
```

### Arguments

 `dp` A decision problem object constructed by calling `sequential.dp`. `mins` A numeric, atomic vector specifying the lower boundary of the grid points for each dimension of the state vector. `maxs` A numeric, atomic vector specifying the upper boundary of the grid points for each dimension of the state vector. `steps` A numeric, atomic vector specifying the step size between grid points for each dimension of the state vector. `n.sims` A numeric, atomic vector of length equal to `dp\$n.stages` specifying the number of simulation draws to perform at each stage. `state.start` An optional start value for the state. If provided, this value effectively determines a fixed prior for the parameter of the decision problem (before the first stage). The first stage computations will then only be performed for this particular value. If the default value `NA` is used, computations for the first stage will be performed for all grid points, as for the subsequent stages.

### Value

If `state.start` equals `NA`, then the value returned is a list with components

 `opt.decision` Function taking a stage and a state into the optimal decision corresponding to the closest grid point at that stage. `opt.utility` Function taking a stage and a state into the optimal expected utility corresponding to the closest grid point at that stage.

If an explicit value for `state.start` is provided, the value returned is a list with components

 `opt.stage1.decision` Optimal stage 1 decision. `opt.stage1.utility` Optimal stage 1 utility. `opt.decision` Function taking a stage (greater than 1) and a state into the optimal decision corresponding to the closest grid point at that stage. `opt.utility` Function taking a stage (greater than 1) and a state into the optimal expected utility corresponding to the closest grid point at that stage.

### Author(s)

Sebastian Jobjörnsson jobjorns@chalmers.se

`optimise.sequential.normal.eu`