:orphan:

beta
****

Specifies the degree to which previous experiences (v-values) are considered in the decision function,
in other words, how much weight is placed on the v-values in the decision function.
A low value for ``beta`` means high exploration.

The value of the parameter ``beta`` is used in :ref:`the decision function<the-decision-function>`. See also :doc:`mu`.

The parameter ``beta`` can be either a single value, in which case the same weight is placed on all v-values, or
specified per element-behavior pair. Wildcards (*) may be used to set several values at once.

Syntax
------

::

  beta = e1->b1: v1, e1->b2: v2, ..., en->bn: vn, default: d
  beta = v1
  beta = *->*:v1  # Same as above
  beta = e1->*:v1
  beta = *->b1:v1

where ``v1,v2,...,vn`` and ``d`` are :ref:`scalar expressions<scalar-expressions>`.

Description
-----------

``beta = e1->b1: v1, e1->b2: v2, ..., en->bn: vn, default: d`` sets the individual weight on

- v(e1->b1) to v1,
- v(e1->b2) to v2, ...,
- v(en->bn) to v2,

and the weight for all other v-values to d.

- The specification is independent of the list order:

  ``beta = e1->b1:v1, e1->b2:v2, default:d``

  is the same as

  ``beta = e1->b2:v2, default:d, e1->b1:v1``.

- ``default`` need not be specified if all possible combinations ``element->behavior`` are present in the list. For example,

  ::

    stimulus_elements = e1, e2
    behaviors = b1, b2
    beta = e1->b1:v11, e1->b2:v12, e2->b1:v21, e2->b2:v22

----

``beta = v1`` sets the weight for all v-values to v1.

- ``beta = v1`` is the same as ``beta = default: v1``.

Dependencies
------------

- The properties ``stimulus_elements`` and  ``behaviors`` must be specified before ``beta``.
- Each stimulus element used in the specification of ``beta`` must be present in the parameter ``stimulus_elements``.
- Each behavior used in the specification of ``beta`` must be present in the parameter ``behaviors``.

Examples
--------

::

  @variables x = 1
  beta = element1->behavior1: x, element1->behavior2: x+1, default:x+2

sets the weight for v(element1->behavior1) to 1 and for v(element1->behavior1) to 2, and
for the remaining possible element-behavior pairs to 3.

::

  beta = element1->behavior1: 0.5, default:0

sets the weight for v(element1->behavior1) to 0.5, and for the remaining possible element-behavior pairs to 3.

::

  beta = 0.1

sets the weight for all v-values to 0.1.