Inclusion Criteria:
1. age 55-85 years;
2. moderate to severe OSA as defined by an AHI ≥ 15 events/hr, or no apnea defined by an AHI\<5 events/hr using American Academy of Sleep Medicine (AASM) diagnostic methodology as determined on a diagnostic polysomnography;
3. Scoring education adjusted scores 28-35 (inclusive) on optional Telephone Interview for Cognitive Status Modified (pre-screen);
4. Scoring 0-0.5 on the Clinical Dementia Rating Scale (CDR);
5. Scoring 23-30 on the Mini Mental State Examination (MMSE) (exceptions may be made for participants with \<8 years of education as determined by the clinical research team);
6. Memory impairment approximately 1.0-1.5 standard deviations below normal (adjusted for age and education) determined by scores on the Logical Memory II a test from the Wechsler memory scale;
7. permitted medications (antidepressants, etc.) stable for at least 4 weeks (12 weeks for cholinesterase inhibitors/memantine) as per ADNI3 criteria;
8. Non-depressed: Scoring \< 6 on the Geriatric Depression Scale;
9. study partner, defined as an informant/caregiver who will be able to answer questions about the study participant, and meets one of the following criteria: (a) lives with the participant; (b) spends at least 3 times per week in-person contact with the participant; (c) spends at least 3 times per week in phone contact with the participant; or (d) spends at least 10 hours per week in any combination of phone or in person contact;
10. adequate visual and auditory acuity to allow testing;
11. Post-menopause or surgically sterile;
12. testability - willing and able to complete baseline, 6-month, and 1-year outcome measures, and willing to send in the CPAP Smartcard for adherence;
13. completed at least 6 grades of education; and
14. fluent in English or Spanish.
Exclusion Criteria:
1. any significant neurologic disease other than aMCI, such as Parkinson's Disease, Huntington's disease, normal pressure hydrocephalus, progressive supranuclear palsy, multiple sclerosis, head trauma followed by permanent neurologic deficits or known congenital brain structure abnormalities; within the past 6 months brain tumor, or seizure disorder, or subdural hematoma, or post-stroke (based on Modified Hachinski Ischemic Score);
2. Optional: MRI exclusions - presence of pacemakers, aneurysm clips, artificial heart valves, ear implants, metal fragments or foreign objects in the eyes, skin, or body; however, the participant has the option of participating in the study without having an MRI;
3. psychiatric disorders, including uncontrolled major depression, newly diagnosed or exacerbation in past 6 months of bipolar disorder as described in the DSM-IV, psychotic features, agitation or behavioral problems within the past 6 months that could lead to difficulty complying with the protocol, or history of schizophrenia (DSM-IV criteria);
4. history of alcohol abuse or dependence within the past 6 months (DSM-IV criteria);
5. any current significant systemic illness or unstable medical condition that could lead to difficulty in complying with the protocol (such as unstable cardiovascular disease); current use of supplemental oxygen or hypoxemia indicated by documented daytime oxyhemoglobin saturation \<90% on room air, uncontrolled thyroid disease (to be included must be on stable dose of thyroid medication for \>6 months), uncontrolled cirrhosis, cancer diagnosis within the past 6 months (exceptions may be made at the PI's discretion depending on cancer severity and the treatment required), clinically significant laboratory abnormalities such as reported untreated folate, B12, or TSH disease, or resident of a skilled nursing facility;
6. participation in clinical studies involving neuropsychological measures being conducted more than twice a year;
7. received and was adherent to CPAP or bi-level pressure for OSA within the past 6 months;
