Do I need to reimburse my employee for buying, without prior approval, very expensive safety shoes when we provide reasonably adequate shoes to employees?

No, you are not required to reimburse the employee in this situation.

• Labor Code Section 6401 requires employers to provide safety devices and safeguards that are reasonably adequate to render the workplace safe.
• Labor Code Section 2802 requires reimbursement only for “necessary expenditures” and “reasonable costs” incurred in the direct discharge of duties.

Since your company already provides reasonably adequate safety shoes, and the employee purchased expensive shoes without prior approval or following company policy, the cost is unlikely to be considered “reasonable” under Section 2802. You may offer replacement shoes