Cal. Civ. Proc. Code § 1297.318

(a) Unless otherwise agreed by the parties, the costs of an arbitration shall be at the discretion of the arbitral tribunal.
(b) In making an order for costs, the arbitral tribunal may include as costs any of the following:
1. (1) The fees and expenses of the arbitrators and expert witnesses.
2. (2) Legal fees and expenses.
3. (3) Any administration fees of the institution supervising the arbitration, if any.
4. (4) Any other expenses incurred in connection with the arbitral proceedings.
(c) In making an order for costs, the arbitral tribunal may specify any of the following:
1. (1) The party entitled to costs.
2. (2) The party who shall pay the costs.
3. (3) The amount of costs or method of determining that amount.
4. (4) The manner in which the costs shall be paid.