trueskill-tt/tests/reconvergence_equivalence.rs

//! Converging, appending, and converging again must reach the same fixed point
//! as converging once over the whole event set.
//!
//! `tests/ingestion_equivalence.rs` covers a different question: it varies how
//! events are *batched* but converges only at the end. This file converges
//! between batches, which is the path a caller takes when it fits, serves for a
//! while, then ingests more.
//!
//! The property matters beyond ergonomics. It says `converge` reaches a fixed
//! point determined by the events, ratings and configuration alone — not by the
//! message state it started from. That is what makes a restored snapshot safe:
//! an inexact one cannot corrupt the answer, only cost an extra sweep. See #45.

use smallvec::smallvec;
use trueskill_tt::{ConvergenceOptions, Event, Gaussian, History, Member, Outcome, Team};

fn tight() -> ConvergenceOptions {
    ConvergenceOptions {
        max_iter: 5_000,
        epsilon: 1e-12,
        alpha: 1.0,
    }
}

fn ev(a: &str, b: &str, time: i64) -> Event<i64, String> {
    Event {
        time,
        teams: smallvec![
            Team::with_members([Member::new(a.to_string())]),
            Team::with_members([Member::new(b.to_string())]),
        ],
        outcome: Outcome::winner(0, 2),
    }
}

/// Ingest each chunk in turn, converging fully after every one.
fn fit_in_chunks(chunks: Vec<Events>) -> Vec<(String, Gaussian)> {
    let mut h: History<i64, _, _, String> =
        History::builder_with_key().convergence(tight()).build();

    for chunk in chunks {
        h.add_events(chunk).unwrap();
        let report = h.converge().unwrap();
        assert!(
            report.converged,
            "a chunk failed to converge, so any comparison would be measuring \
             truncation rather than the fixed point; final step {:?}",
            report.final_step
        );
    }

    let mut skills: Vec<(String, Gaussian)> = h
        .learning_curves()
        .into_iter()
        .map(|(k, curve)| (k, curve.last().unwrap().1))
        .collect();
    skills.sort_by(|a, b| a.0.cmp(&b.0));
    skills
}

fn assert_same(a: &[(String, Gaussian)], b: &[(String, Gaussian)], what: &str) {
    assert_eq!(a.len(), b.len(), "{what}: competitor count differs");
    for ((ka, ga), (kb, gb)) in a.iter().zip(b) {
        assert_eq!(ka, kb, "{what}: key order differs");
        // Measured: 6.2e-13 for a later append, 8.9e-11 for an interleaved one.
        // The bar is well clear of both but far under anything that would let a
        // genuine divergence through.
        assert!(
            (ga.mu() - gb.mu()).abs() < 1e-8 && (ga.sigma() - gb.sigma()).abs() < 1e-8,
            "{what}: {ka} differs — one-shot mu={} sigma={}, chunked mu={} sigma={}",
            ga.mu(),
            ga.sigma(),
            gb.mu(),
            gb.sigma()
        );
    }
}

type Events = Vec<Event<i64, String>>;

/// Two chunks of events: the first at times 0..20, the second at 100..120.
fn fixture() -> (Events, Events) {
    let names = ["a", "b", "c", "d", "e"];
    let mut seed = 7u64;
    let mut rnd = move || {
        seed ^= seed << 13;
        seed ^= seed >> 7;
        seed ^= seed << 17;
        seed
    };

    let (mut early, mut late) = (Vec::new(), Vec::new());
    for t in 0..40i64 {
        let i = (rnd() % 5) as usize;
        let mut j = (rnd() % 5) as usize;
        if j == i {
            j = (j + 1) % 5;
        }
        if t < 20 {
            early.push(ev(names[i], names[j], t));
        } else {
            late.push(ev(names[i], names[j], 100 + t));
        }
    }
    (early, late)
}

/// The ordinary case: new events are strictly later than everything fitted.
#[test]
fn appending_later_events_matches_a_single_fit() {
    let (early, late) = fixture();
    let all: Vec<_> = early.iter().cloned().chain(late.iter().cloned()).collect();

    assert_same(
        &fit_in_chunks(vec![all]),
        &fit_in_chunks(vec![early, late]),
        "append strictly later",
    );
}

/// The case the design question suspected might be weaker: appended events
/// interleave with slices that are already fitted, so the append legitimately
/// revises the past. It is not weaker — Through Time revises the past on every
/// converge regardless, so there is nothing special about doing it in two steps.
#[test]
fn appending_interleaved_events_matches_a_single_fit() {
    let (early, late) = fixture();
    let all: Vec<_> = early.iter().cloned().chain(late.iter().cloned()).collect();

    // Split by parity so the second chunk is back-dated into the first's range.
    let first: Vec<_> = all.iter().step_by(2).cloned().collect();
    let second: Vec<_> = all.iter().skip(1).step_by(2).cloned().collect();
    let together: Vec<_> = first
        .iter()
        .cloned()
        .chain(second.iter().cloned())
        .collect();

    assert_same(
        &fit_in_chunks(vec![together]),
        &fit_in_chunks(vec![first, second]),
        "append interleaved",
    );
}

/// Converging an already-converged history is a no-op, which is what makes a
/// restored snapshot worth having: the work is skipped rather than redone.
#[test]
fn re_converging_an_unchanged_history_costs_one_iteration() {
    let (early, late) = fixture();
    let all: Vec<_> = early.into_iter().chain(late).collect();

    let mut h: History<i64, _, _, String> =
        History::builder_with_key().convergence(tight()).build();
    h.add_events(all).unwrap();
    let first = h.converge().unwrap();
    assert!(first.converged);

    let again = h.converge().unwrap();
    assert_eq!(
        again.iterations, 1,
        "a converged history should settle immediately, not re-grind"
    );
    assert!(again.converged);
}