# ExpStepSize { #phasic.svgd.ExpStepSize }

```python
phasic.svgd.ExpStepSize(first_step=0.01, last_step=1e-06, tau=1000.0)
```

Exponential decay schedule: step_size = first_step * exp(-iteration/tau) + last_step * (1 - exp(-iteration/tau)).

This schedule helps prevent divergence with large datasets by gradually reducing
the step size as optimization progresses.

## Parameters {.doc-section .doc-section-parameters}

<code>[**first_step**]{.parameter-name} [:]{.parameter-annotation-sep} [[float](`float`)]{.parameter-annotation} [ = ]{.parameter-default-sep} [0.01]{.parameter-default}</code>

:   Initial (first) step size at iteration 0

<code>[**last_step**]{.parameter-name} [:]{.parameter-annotation-sep} [[float](`float`)]{.parameter-annotation} [ = ]{.parameter-default-sep} [1e-6]{.parameter-default}</code>

:   Final (last) step size as iteration → ∞

<code>[**tau**]{.parameter-name} [:]{.parameter-annotation-sep} [[float](`float`)]{.parameter-annotation} [ = ]{.parameter-default-sep} [1000.0]{.parameter-default}</code>

:   Decay time constant (larger = slower decay)

## Examples {.doc-section .doc-section-examples}

```python
>>> schedule = ExpStepSize(first_step=0.1, last_step=0.01, tau=500.0)
>>> schedule(0)      # iteration 0
0.1
>>> schedule(500)    # iteration 500 (≈63% decay)
0.037
>>> schedule(5000)   # iteration 5000 (full decay)
0.01
```