To Evaluate the Safety and Efficacy of Ipatasertib (GDC-0068) in Combination With Paclitaxel in Platinum-resistant Recurrent Epithelial Ovarian Cancer

Inclusion Criteria: * Provision of signed and dated, written informed consent prior to any study specific procedures, sampling and analyses o If a patient declines to participate in any voluntary exploratory research and/or genetic component of the study, there will be no penalty or loss of benefit to the patient and he/she will not be excluded from other aspects of the study * Aged at least 18 years at time of signing informed consent * A pathologic (histology or cytology) confirmed diagnosis of epithelial ovarian cancer, including fallopian or primary peritoneal cancer o low grade serous histology is excluded * Radiographic evidence of recurrent epithelial ovarian cancer (ovarian, fallopian tube, or primary peritoneal cancer) that has become "platinum-resistant," defined as progression of disease within 6 months from the last dose of platinum-based chemotherapy, or platinum refractory * Not a candidate for cytoreductive surgery * Measurable disease (at least one lesion that can be accurately assessed repeatedly by CT or MRI) as evidenced on pre-treatment baseline CT of Chest/Abdomen/Pelvis, MRI, or PET/CT, or evaluable disease (defined as anything non-measurable- pleural effusions, lesions \<1cm, etc). * World Health Organization (WHO) performance status 0-1 with no deterioration over the previous 2 weeks and minimum life expectancy of 12 weeks * Up to 3 lines of prior cytotoxic chemotherapy * Previously received bevacizumab * Has not received weekly paclitaxel-containing regimen, EXCEPT for in the front-line setting o Patients with prior paclitaxel reactions may be enrolled if they have been successfully re-treated with steroid pre-medication in the past * Patients must use adequate contraceptive measures, should not be breast feeding and must have a negative pregnancy test prior to start of dosing (within 7 days) if of child-bearing potential or must have evidence of non-child-bearing potential by fulfilling one of the following criteria at screening: * Post-menopausal defined as aged more than 50 years and amenorrhea for at least 12 months following cessation of all exogenous hormonal treatments * Documentation of irreversible surgical sterilization by hysterectomy, bilateral oophorectomy or bilateral salpingectomy but not tubal ligation * For women of childbearing potential: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive methods with a failure rate of \< 1% per year during the treatment period and for 28 days after the last dose of study treatment. Women must refrain from donating eggs during this same period. Exclusion Criteria: * Treatment with any of the following: * Any investigational agents or study drugs from a previous clinical study within 28 days of the first dose of study treatment * Any other chemotherapy, immunotherapy or anticancer agents within 14 days of the first dose of study treatment * Potent inhibitors or inducers or substrates of CYP3A4 or substrates of CYP2D6 within 2 weeks before the first dose of study treatment (3 weeks for St John's Wort) * Any prior exposure to Ipatasertib * Major surgery (excluding placement of vascular access) within 4 weeks of the first dose of study treatment * Radiotherapy with a wide field of radiation within 4 weeks or radiotherapy with a limited field of radiation for palliation within 2 weeks of the first dose of study treatment * With the exception of alopecia, any unresolved toxicities from prior therapy greater than Common Terminology Criteria for Adverse Events (CTCAE) grade 1 at the time of starting study treatment * Spinal cord compression or brain metastases unless asymptomatic, treated and stable and not requiring steroids for at least 2 weeks prior to start of study treatment * Concurrent use of endocrine therapy * As judged by the investigator, any evidence of severe or uncontrolled systemic diseases, including active bleeding diatheses, or active infection including hepatitis B, hepatitis C and human immunodeficiency virus (HIV). Screening for chronic conditions is not required. * Any of the following cardiac criteria: * Any clinically important abnormalities in rhythm, known prolonged QTc, conduction or morphology of resting ECG, complete left bundle branch block, third degree heart block * Experience of any of the following procedures or conditions in the preceding 6 months: coronary artery bypass graft, angioplasty, vascular stent, myocardial infarction, angina pectoris, congestive heart failure NYHA Grade 2 or greater * Uncontrolled hypotension - Systolic BP \<90mmHg and/or diastolic BP \<50mmHg * Left ventricular ejection fraction (LVEF) below lower limit of normal for site * Inadequate bone marrow reserve or organ function as demonstrated by any of the following laboratory values: * Absolute neutrophil count \< 1.5 x 109/L * Platelet count \< 100 x 109/L * Hemoglobin \< 9 g/L * Alanine aminotransferase \> 2.5 times the upper limit of normal (ULN) * Aspartate aminotransferase \> 2.5 times ULN * Total bilirubin \> 1.5 times ULN * Creatinine \>1.5 times ULN concurrent with creatinine clearance \< 50 ml/min (measured or calculated by Cockcroft and Gault equation); confirmation of creatinine clearance is only required when creatinine is \> 1.5 times ULN * Proteinuria 3+ on dipstick analysis or \>500mg/24 hours * Sodium or potassium outside normal reference range for site * Peripheral neuropathy grade 2 or greater * Refractory nausea and vomiting, chronic gastrointestinal diseases, inability to swallow the formulated product or previous significant bowel resection that would preclude adequate absorption Ipatasertib * History of hypersensitivity to Ipatasertib, or drugs with a similar chemical structure or class to Ipatasertib * Clinically significant abnormalities of glucose metabolism as defined by any of the following: * Diagnosis of type I or type II diabetes mellitus requiring insulin * A baseline fasting glucose value of ≥ 200 mg/dL (fasting glucose value to be obtained only if non-fasting glucose \>200mg/dL) * Glycosylated hemoglobin (HbA1C) \>7.5% * Uncontrolled pleural effusion, pericardial effusion, or ascites * Other malignancies within the past 3 years, with the exception of adequately resected basal or squamous carcinoma of the skin * Clinically significant pulmonary symptoms or disease * Judgment by the investigator that the patient should not participate in the study if the patient is unlikely to comply with study procedures, restrictions and requirements