83 lines
3.0 KiB
Markdown
83 lines
3.0 KiB
Markdown
# TrueSkill - Through Time
|
||
|
||
Rust port of [TrueSkillThroughTime.py](https://github.com/glandfried/TrueSkillThroughTime.py).
|
||
|
||
## Other implementations
|
||
|
||
- [ttt-scala](https://github.com/ankurdave/ttt-scala)
|
||
- [ChessAnalysis #F](https://github.com/lucasmaystre/ChessAnalysis)
|
||
- [TrueSkillThroughTime.jl](https://github.com/glandfried/TrueSkillThroughTime.jl)
|
||
- [TrueSkillThroughTime.R](https://github.com/glandfried/TrueSkillThroughTime.R)
|
||
- [TrueSkill Through Time: Revisiting the History of Chess](https://www.microsoft.com/en-us/research/wp-content/uploads/2008/01/NIPS2007_0931.pdf)
|
||
- [TrueSkill Through Time. The full scientific documentation](https://glandfried.github.io/publication/landfried2021-learning/)
|
||
|
||
## Drift
|
||
|
||
Skill drift models how a player's true skill can change between appearances. Each time a player reappears after a gap, their skill uncertainty is widened by the drift model before the new evidence is incorporated.
|
||
|
||
Drift is represented by the `Drift` trait:
|
||
|
||
```rust
|
||
pub trait Drift: Copy + Debug {
|
||
fn variance_delta(&self, elapsed: i64) -> f64;
|
||
}
|
||
```
|
||
|
||
`variance_delta` returns the amount to add to `σ²` given the elapsed time since the player last played. Internally, `Gaussian::forget` uses this to compute the new sigma: `σ_new = sqrt(σ² + variance_delta)`.
|
||
|
||
### ConstantDrift
|
||
|
||
The built-in `ConstantDrift` implements a linear random walk — skill uncertainty grows proportionally to time:
|
||
|
||
```
|
||
variance_delta = elapsed * γ²
|
||
```
|
||
|
||
This is the standard TrueSkill Through Time model. Use it by passing a `ConstantDrift(gamma)` when constructing a `Player`:
|
||
|
||
```rust
|
||
use trueskill_tt::{Player, Gaussian, drift::ConstantDrift};
|
||
|
||
// gamma = 0.1 means skill can shift ~0.1 per time unit
|
||
let player = Player::new(Gaussian::from_ms(0.0, 6.0), 1.0, ConstantDrift(0.1));
|
||
```
|
||
|
||
### Custom drift
|
||
|
||
Implement `Drift` to express any other model. For example, a drift that saturates after a long absence (uncertainty grows with the square root of elapsed time instead of linearly):
|
||
|
||
```rust
|
||
use trueskill_tt::drift::Drift;
|
||
|
||
#[derive(Clone, Copy, Debug)]
|
||
struct SqrtDrift {
|
||
gamma: f64,
|
||
}
|
||
|
||
impl Drift for SqrtDrift {
|
||
fn variance_delta(&self, elapsed: i64) -> f64 {
|
||
(elapsed as f64).sqrt() * self.gamma * self.gamma
|
||
}
|
||
}
|
||
|
||
let player = Player::new(Gaussian::from_ms(0.0, 6.0), 1.0, SqrtDrift { gamma: 0.5 });
|
||
```
|
||
|
||
To use a custom drift type with `History`, use the `.drift()` builder method instead of `.gamma()`:
|
||
|
||
```rust
|
||
let h = History::builder()
|
||
.drift(SqrtDrift { gamma: 0.5 })
|
||
.build();
|
||
```
|
||
|
||
## Todo
|
||
|
||
- [x] Implement approx for Gaussian
|
||
- [x] Add more tests from `TrueSkillThroughTime.jl`
|
||
- [ ] Add tests for `quality()` (Use [sublee/trueskill](https://github.com/sublee/trueskill/tree/master) as reference)
|
||
- [ ] Benchmark Batch::iteration()
|
||
- [ ] Time needs to be an enum so we can have multiple states (see `batch::compute_elapsed()`)
|
||
- [ ] Add examples (use same TrueSkillThroughTime.(py|jl))
|
||
- [ ] Add Observer (see [argmin](https://docs.rs/argmin/latest/argmin/core/trait.Observe.html) for inspiration)
|