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Here is another stable algorithm for losing weight, which is fully compatible with cardio.

Choose a desired rate of weight loss and a measurement period. Each period, measure your inputs and do the following:

    IF (weight_loss_rate < desired_rate)
      input -= 200 cals
    ELSE
      input += 50 cals
    END
After following this algorithm, your caloric intake will converge to the region [optimal rate - 150, optimal rate + 50]. This is true even accounting for noise in the measurements - that just smears out the -150 and +50 a bit.

The nice thing about bodyweight is that it's a stable monotonic dynamical system. Noise and uncertainty don't hurt you much provided you build robust controls.



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