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Learned lifetime distribution

Learned lifetime distribution is the prediction unit of emitting a probability distribution over remaining lifetime rather than a point estimate. A VM-lifetime predictor that outputs "this VM will run for 4 hours" emits a point; one that outputs a distribution over remaining hours (e.g. a mixture of exponentials, a quantile set, or parameters of a parametric family) emits a learned distribution.

Named in the 2025-10-17 Google LAVA post — the "L" in LAVA stands for Lifetime-Aware VM Allocation and the paper's title is "Lifetime-Aware VM Allocation with Learned Distributions and Adaptation to Mispredictions" (Source: sources/2025-10-17-google-solving-virtual-machine-puzzles-lava).

Why a distribution, not a point

Three reasons all load-bearing in the LAVA framing:

  • Downstream decisions are cost-asymmetric in the prediction error. A too-long lifetime estimate that holds a host open is not the same cost as a too-short one that forces premature eviction. Point prediction can't express this; distributions let the consumer pick a quantile matched to the asymmetry (e.g. use P90 of remaining lifetime when overestimation is cheaper than underestimation).
  • Risk-aware placement requires tail information. "Will this VM still be running 24 hours from now?" is a probability query, not a mean query. A scheduler that wants to preserve empty hosts needs P(lifetime > threshold), not E[lifetime].
  • Uncertainty-gated rescheduling needs calibrated width. LARS only fires when the updated prediction is confident enough to justify the migration cost. The confidence signal comes from the distribution's width — impossible to extract from a point.

Representation choices

The raw post doesn't specify the representation; the linked arXiv paper is the source for specifics. Common shapes from the surrounding literature:

  • Parametric — predict parameters of a fixed family (e.g. lognormal(μ, σ), mixture of exponentials).
  • Quantile regression — predict a fixed set of quantiles (P10, P50, P90) directly.
  • Histogram / discretised — predict a probability over bucketed remaining-lifetime bins.
  • Survival-analysis shapes — hazard function / Kaplan- Meier-style estimators that naturally emit lifetime distributions.

Relationship to

uncertainty quantification

Learned lifetime distributions are a special case of uncertainty-quantified prediction: the prediction target is lifetime, and the distribution is the uncertainty representation. Calibration (does the empirical frequency of lifetime > q match the predicted P(lifetime > q)?) is the load-bearing property — uncalibrated distributions are decorative, not actionable.

The 2025-07-29 Google RLM post frames the same discipline at a different target: the RLM sampled-decoder mechanism produces calibrated uncertainty on MIPS-per-GCU predictions. Both posts use "calibrated distribution over target" as the primitive that makes downstream risk-aware decisions legitimate.

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