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What “worst case” actually means

Declare an ambiguity set, let the system grow out of it, then watch three predictors face two kinds of truth.
Who it is for You want the central semantics of DRPP, not just the API
Prerequisites The idea of an ambiguity set; nothing from the papers
Runs on pip install ppsds — this page uses the core only

One ambiguity set, two meanings of “worst”

python examples/understand_drpp_on_simulated_ambiguity/quickstart.py

A few seconds, single process, core API only: no cache, no command line, no model table. It declares a conic-moment ambiguity set by hand, then runs the same rollout loop under two semantics:

  • random — one SDS is sampled from the set and shared by every predictor, so only the noise differs.
  • worst — each predictor faces the SDS chosen specifically against it, a best response. This is the paper's central semantics.

Eig-DRPP dominates the runtime because it solves a cone program at every step; lower N_TRAJ or T in the file to make it faster.

Mean logarithmic score (higher is better), 4 trajectories x 50 steps

predictor       random     worst
--------------------------------
Nominal         -4.726   -23.365
Noise-DRPP      -3.974   -10.186
Eig-DRPP        -4.566    -5.541

Theoretical bounds (per step): upper -4.048, lower -5.833

What to conclude: under random the three predictors sit close together: the nominal model is roughly right, so robustness buys little and costs a little. Under worst they separate sharply: Nominal is driven down to -23.4 because it is attacked on purpose, while Eig-DRPP shrinks its covariance along the worst direction and holds near its lower bound of -5.833. That gap is the guarantee, measured: average performance given up under random, worst-case floor collected under worst. Noise-DRPP sits in between, which is what “robust to noise only” buys.

The two bounds printed at the end are the within-one-set pair (value_upper_bound_true_transition / value_lower_bound_eigvec_fixed). They are not the “predictability ceiling versus DRPP floor” pair; Research keeps the two straight.

The same set, at production size

The teaching script is deliberately small. Reproducing the paper's sweeps needs seven models, a validated cache, and multiple processes — that is a separate experiment, kept out of this example so the example stays readable:

DRPP on simulated ambiguity →

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