mc_sgd
======

.. py:function:: t3toolbox.optimizers.mc_sgd(geometry, kind, sample, data, x0, rng, batch, order = None, weight = None, draw = None, use_jit = False, regularizer = None, chunk_size = 'auto', **kwargs)

   .. code-block:: python

      def mc_sgd(
              geometry,                       # ragged/uniform MANIFOLD (intended) / COREWISE (must match x0)
              kind:     str,                  # 'apply' / 'entries' / 'probe' (+ '_derivatives')
              sample:   typ.Any,              # ww / index, or (ww, pp) / (index, pp) for derivatives
              data:     typ.Any,             # observed values to fit
              x0:       Point,                # initial point
              rng,                            # np.random.Generator -- passed to the draw each step
              batch:    int,                  # measurements per minibatch (default flat draw; ignored if draw given)
              order:    typ.Optional[int] = None,
              weight:   typ.Optional[typ.Any] = None,   # residual weight ω: per-mode (probe) / ω[mode,order] (derivatives)
              draw:     typ.Optional[typ.Callable]        = None,  # custom draw(rng)->(sample_B,data_B); None = flat
              use_jit:  bool = False,         # jit the per-step kernel: auto-converts x0/sample/data to jax -> a jax-backed float32 result; raises if jax absent
              regularizer: typ.Any = None,    # optional regularizer, e.g. optimizers.IdentityRegularizer(λ) (ragged only); scaled by batch/n per step
              chunk_size: typ.Any = 'auto',   # probe_derivatives 𝒥ᵀ memory chunk; 'auto' -> estimate_chunk_size (docs/chunking.md)
              **kwargs,                       # forwarded to backend.optimizers.mc_sgd (max_iter, check_every, ...)
      ) -> typ.Tuple[Point, dict]:


   Manifold Cauchy SGD -- minibatched, tuning-free Cauchy step. Ragged or uniform ``x0`` (see
   :py:func:`gradient_descent`). A ``regularizer`` (ragged only) is scaled by ``batch/n`` per step so
   ``λ`` matches the full-batch optimizers. See :py:func:`t3toolbox.backend.optimizers.mc_sgd`.